Forces proportional to AB, BC and 2CA act along the sides of a triangle ABC in order . Their resultant is represented in magnitude and direction By
If a particle moves from point P (2, 3, 5) to point Q (3, 4, 5). Its displacement vector be
The angle between two vectors − 2 i ^ + 3 j ^ + k ^ and 2 i ^ + 2 j ^ − 4 k ^ is
If |A| = 2 and |B| = 4, then match the relation in Column I with the angle θ between A and B in column II. Column I Column II (p) A.B = 0 (i) θ = 0 (q) A.B = +8 (ii) θ = 90 0 r A.B = 4 (iii) θ = 180 0 (s) A.B = -8 (iv) θ = 60 0 Now, mark the correct choice from the given codes. Codes
Consider a vector F = 4 i ^ − 3 j ^ . Another vector that is perpendicular to F is
If u ^ 1 and u ^ 2 are two unit vectors and | u ^ 1 × u ^ 2 | = 3 ( u ^ 1 . u ^ 2 ) then the value of u ^ 1 + u ^ 2 is
Statement I : The difference of two vectors A and B can be treated as the sum of two vectors. Statement II : Subtraction of vectors can be defined in terms of addition of vectors.
A vector perpendicular to both the vectors 2 i ^ − 3 j ^ and 3 i ^ − 2 j ^ is
The resultant of two vectors P and Q is R . If Q is doubled, the new resultant is perpendicular to P . Then, R equal to
If a vector 2 i ^ + 3 j ^ + 8 k ^ is perpendicular to the vector 4 j ^ – 4 i ^ + α k ^ , then the value of α . is
If the sum of two unit vectors is a unit vector, then magnitude of difference in two unit vectors is
There are N coplanar vectors each of magnitude V. Each vector is inclined to the preceding vector at angle 2 π N . What is the magnitude of their resultant?
Which of the following is a unit vector?
Two forces P and Q have a resultant perpendicular to P . The angle between the forces is
A vector 2 i ^ + 2 j ^ rotated about its tail through an angle 45 0 in clockwise direction. Then the new vector is
If two vectors 2 i ^ + 3 j ^ + k ^ and – 4 i ^ – 6 j ^ – λ k ^ are parallel to each other, then value of λ is
Vector P = 6 i ^ + 4 2 j ^ + 4 2 k ^ makes an angle with Z-axis which is equal to
If vectors A and B have an angle θ between them, then value of | A ^ – B ^ | will be
The resultant of three vectors 1, 2 and 3 units whose directions are those of the sides of an equilateral triangle is
Two vectors P and Q are inclined to each other at angle θ . Which of the following is the unit vector perpendicular to P and Q ?
If | A × B | = 3 ( A ⋅ B ) then the value of | A × B | is
The vector a = 2 i ^ rotates anticlockwise in xy-plane through an angle of 90 o . Then change produced in the vector is —-
Maximum and minimum magnitude of the resultant of two vectors of magnitudes P and Q are in the ratio 3 : 1 Which of the following relations is true?
If | A + B | = | A − B |, then the angle between A and B will be
P + Q is a unit vector along x-axis. If P = i ^ − j ^ + k ^ , then what is Q?
Unit vector parallel to the resultant of vectors A = 4 i ^ − 3 j ^ and B = 8 i ^ + 8 j ^ will be
The angle between the two vectors A = 3 i ^ + 4 j ^ + 5 k ^ and B = 3 i ^ + 4 j ^ + 5 k ^ is
Statement I : Minimum number of non-equal vectors in a plane required to give zero resultant is three. Statement II : If A + B + C = 0 , then they must lie in one plane.
If the angle between the vectors A and B is θ , the value of the product ( B × A ) . A is equal to
Statement I : If θ be the angle between A and B , then tanθ = A × B A . B Statement II : A × B is perpendicular to A . B
Statement I : Multiplying any vector by an scalar is a meaningful operations. Statement II : In uniform motion speed remains constant.
If and .Find the angle between the two vectors.
What is the maximum value y = 5 sin x -2 6 cos x?
Select correct alternatives. (i) 1 rad= 57.3 degree (ii) 1degree = 60 minute (iii) 1 minute = 60 seconds (iv) 1 right angle = 90 degree
The forces, which meet at one point but their lines of action do not lie on one plane, are called
Consider a vector F = 4 i ^ – 3 j ^ . Another vector perpendicular to F is
Which of the following is correct?
A vector is represented by 3 i ^ + j ^ + 2 k ^ . Its length in XY-plane is
The area Of the parallelogram represented by the vectors A = 2 i ^ + 3 j ^ and B = i ^ + 4 j ^ is
Let A = i ^ A cos θ + j ^ A sin θ be any vector. Another vector B which is perpendicular to A can be expressed as
If A . B = 0 and A X B = 1, then A and B are
If the sum of two unit vectors is a unit vector, then magnitude of difference in two unit vectors is
The sum of two vectors A and B is at right. angles to their difference. Then, the correct relation is
There are N coplanar vectors each of magnitude V. Each vector is inclined to the preceding vector at angle 2 π N . What is the magnitude of their resultant?
A vector having magnitude 30 unit makes equal angles with each of X, Y and Z-axes. The components of vector along each of X, Y and Z-axes are
Forces proportional to AB, BC and 2CA act along the sides of a triangle ABC in order . Their resultant is represented in magnitude and direction by
A unit vector is represented by 0 .5 i ^ + 0 .8 j ^ + c k ^ ,then the value of c is
Two forces P and Q have a resultant perpendicular to P . The angle between the forces is
Which one of the following forces can’t produce Zero resultant
The resultant of A × 0 will be equal to
If p ¯ , q ¯ and r ¯ are three unit vectors represented by the three sides of an equilateral triangle such that p ¯ ⋅ q ¯ + q ¯ . r ¯ = 0 , then which of the following is the correct relation between the three vectors?
With respect to a rectangular cartesian coordinate system, three vectors are expressed as a = 4i-j b = -3i +2j c = -k where i, j, k are unit vectors, along the x, y and z-axis respectively. The unit vector r along the direction of sum of these vectors is
Two forces of magnitudes P and 3 P act at right angles to each other. Their resultant makes an angle θ with P Which of the following gives the correct value of θ ?
If A and B are two vectors and if A x B = B x A, then angle between A and B is
The position vector of a particle is r = ( acos ωt ) i + ( asin ωt ) j The velocity of the particle is
If a vector 2i+3i+8k is perpendicular to the vector 4 i -4j + α k, then the value of α is
The angle between A − B a n d A x B i s ( A ≠ B ) :
The minimum number of vectors having different planes which can be added to give zero resultant is
Rain is falling vertically with a speed of 4 m s – 1 . Wind starts blowing after sometime with a speed of 3 m s – 1 in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella
A force is inclined at 60 0 to the horizontal. If its rectangular component in the horizontal direction is 50 N, then magnitude of the vertical component of force is approximately
The resultant of A + B is R 1 . On reversing the vector B , the resultant becomes R 2 . What is the value of R 1 2 + R 2 2 ?
The three vectors A = 3 i ^ − 2 j ^ + k ^ , B = i ^ − 3 j ^ + 5 k ^ and C = 2 i ^ + j ^ − 4 k ^ form
The magnitude of a given vector with end points (4, -4, 0) and (-2, -2, 0) must be
The vector projection of a vector 3 i ^ + 4 k ^ on y-axis is
The expression ( 1 2 i ^ + 1 2 j ^ ) is a
The unit vector along i ^ + j ^ is
A vector is represented by 3 i ^ + j ^ + 2 k ^ . Its length in XY
If a unit vector is represented by 0 .5 i ^ + 0 .8 j ^ + c k ^ , then the value of ‘c’ is
Determine a vector which when added to the resultant of A = 2 i ^ + 5 j ^ − k ^ and B = 3 i ^ − 4 j ^ − k ^ gives unit vector along negative y direction.
The vector that must be added to the vector i ^ − 3 j ^ + 2 k ^ and 3 i ^ + 6 j ^ − 7 k ^ so that the resultant vector is a unit vector along the y-axis is
The angle between two vectors given by 6 i ^ + 6 j ^ − 3 k ^ and 7 i ^ + 4 j ^ + 4 k ^ is
If P . Q = PQ , then the angle between P and Q
The angles which a vector i ^ + j ^ + 2 k makes with X, Y and Z axes respectively are
The component of vector A = 2 i ^ + 3 j ^ along the vector i ^ + j ^ is
Vector A makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of A ) will be
The torque of the force F = ( 2 i ^ − 3 j ^ + 4 k ^ ) N acting at the point r = ( 3 i ^ + 2 j ^ + 3 k ^ ) m about the origin be
The angle between vectors ( A × B ) and ( B × A ) is
The area of the parallelogram whose sides are represented by the vectors j ^ + 3 k ^ and i ^ + 2 j ^ − k ^ is
The area of a parallelogram whose diagonals are P = 2 i ^ + 3 j ^ and Q = i ^ + 4 j ^ is
The angle between the vectors A and B is θ . The value of the triple product A . ( B × A ) is
Two vector A and B have equal magnitudes. Then the vector A+B is perpendicular to
The vectors from origin to the points A and B are A = 3 i ^ − 6 j ^ + 2 k ^ and B = 2 i ^ + j ^ − 2 k ^ respectively. The area of the triangle OAB be
If | A × B | = 3 A . B , then the value of | A + B | is
Three vectors a , b and c satisfy the relation a . b = 0 and a . c = 0 . The vector a is parallel to
In a methane ( CH 4 ) molecule each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the centre. In coordinates where one of the C-H bonds is in the direction of i ^ + j ^ + k ^ , an adjacent C-H bond is in the i ^ − j ^ − k ^ direction. Then angle between these two bonds.
u ^ 1 , u ^ 2 and u ^ 3 are three unit vector such that u ^ 1 + u ^ 2 + u ^ 3 = 0 . Then the value of u ^ 1 . u ^ 2 − 4 u ^ 3 . u ^ 1 is
| A × B | 2 + | A . B | 2 =
Match the Column I with Column II and select the option from the given code below Column I Column II i. 2 i ^ × i ^ + j ^ p. 2 k ^ ii. 4 i ^ × 2 i ^ − j ^ q. 0 iii. 3 i ^ × 3 i ^ − 4 j ^ r. − 4 k ^ iv. 2 i ^ + j ^ × 2 i ^ s. − 12 k ^ Codes
Statement I : Vector addition is commutative. Statement II : Two vectors may be added graphically using head-to-tail method or parallelogram method.
Statement I : If | A + B | = | A − B | , then angle between A and B is 90 0 Statement II : A + B = B + A
If the vectors A = a i ^ − a j ^ + k ^ a n d B = a i ^ + j ^ − 2 are mutually perpendicular, then positive value of ‘a’ is
If e 1 ^ , e 2 ^ and e 3 ^ are three unit vectors such that e 3 ^ = e 1 ^ + e 2 ^ , Then the value of 3 e 1 ^ . e 3 ^ + 2 e 1 ^ . e 2 ^ is
The magnitude of vector A , B and C are respectively 12, 5 and 13 units and A + B = C then the angle between A and B
A person goes 10 km north and 20 km east. What will be displacement from initial point?
Given that A + B = C and that C is perpendicular to A . Further if | A | = | C | , then what is the angle between A and B ?
In figure, E equals
A vector of magnitude 10 N acting in XY-plane has components 8 N and 6 N along positive X-axis and positive Y-axis, respectively. The coordinate system is rotated about z-axis through angle 90 0 in anti-clockwise direction. Find x-component and y-component in new coordinate system.
Choose the correct statement
A vector is not changed if
The horizontal component of the weight of a body of mass m is
Two vectors of same physical quantity are unequal if a) They have the same magnitude and same direction b) They have different magnitudes but same direction c) They have same magnitude but different directions d) They have different magnitudes and different directions
Consider the following statements A and B given below and identify the correct answer. A) Vectors i ^ + 3 j ^ + 5 k ^ and 2 i ^ + 6 j ^ + 10 k ^ are parallel B) i ^ + j ^ + k ^ represents a unit vector
The resultant of two forces 1 and P is perpendicular to ‘1’ and equal to 1. What is the value of ‘P’ and angle between the forces
If θ is the angle between unit vectors and then is equal to
The value of sum of first hundred natural numbers 1 + 2 + 3 + …. + 100 is :
The value of ( sin 180 ° + cos 90 ° ) 2 is :
If tanθ = 1 5 and θ lies in the first quadrant, the value of cos θ is :
The value of 1 + 1 4 + 1 16 + 1 64 + . . . . . . upto ∞ is :
The length of a string between a kite and a point on the ground is 55 m. If the string makes an angle of 53° from level ground and there is no slack in the string, then the height of the kite is:
For an acute angle 9, sin 8 + cos 8 takes the greatest value when θ is:
Maximum and minimum values of sin x + 3 cos x are respectively :
Bottom end of a ladder leaning against a wall is 3 m away from the foot of the wall as shown in figure, length of the ladder is:
What is the maximum value of 4-cos θ ?
What is the maximum value of 3 cos θ – 4 sin θ ?
What is the minimum value of 2 4 + sin θ + 3 cosθ ?
The equation of shown sinusoidal graph is :
Two vectors A and B are such that A + B = A – B . The angle between the vectors A and B is :
The two vectors A = – 2 i ^ + 3 j ^ + y k ^ and B = i ^ + 2 j ^ + x k ^ are perpendicular. Given x + y = 0 . Find x and y?
Find a vector perpendicular to both the vectors A = i ^ + j ^ and B = j ^ + k ^
The resultant of two vectors P and Q is R . What happen to the new resultant vector is perpendicular to P ⋅ R , when Q is doubled.
Vector P = 6 i ^ + 4 2 j ^ + 4 2 k ^ makes an angle with Z-axis which is equal to
Two vectors A and B inclined at angle θ have a resultant R which makes an angle ϕ with A . If the directions of A and B are interchanged, then the resultant will have the same
If A = B then which· of the following is not correct?
Unit vector parallel to the resultant of vector 8 i ^ arid 8 j ^ will be
The angle between A = i ^ + j ^ and B = i ^ – j ^ is [NCERT Exemplar]
A vector perpendicular to both the vectors 2 i ^ – j ^ + 5 k ^ and X-axis is
If F 1 and F 2 are two vectors of equal magnitudes F such that I F 1 . F 2 I= I F 1 X F 2 |, then IF 1 + F 2 | equals to
If A ^ is a unit vector in a given direction, then the value of A ^ · d A ^ d t is
The angle between the vectors A and B is θ . The value of the triple product A· (B X A) is
If A = 3 i ^ + 4 j ^ and B = 7 i ^ + 24 j ^ the vector having the same magnitude as B and parallel to A is
If two vectors 2 i ^ + 3 j ^ + k ^ and – 4 i ^ – 6 j ^ – λ k ^ are parallel to each other, then value of λ is
The resultant of two vectors 3P and 2P is R. If the first vector is doubled, then the resultant is also doubled. The angle between the two vectors is
What.is the angle between P and the cross product of (P + Q) and (P – Q)?
At what angle must the two forces (x + y) and (x – y) act, so that the resultant may be x 2 + y 2 ?
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is
Two l vectors having equal magnitude , have a resultant equal to either of the two. The angle between them is
The scalar product of two vectors A = 2 i ^ + 2 j ^ – k ^ and B = – j ^ + k ^ , is given by
If A . B = A X B , then angle between A and B is
Consider three vectors A = i ^ + j ^ – 2 k ^ , B = i ^ – j ^ + k ^ and C = 2 i ^ – 3 j ^ + 4 k ^ . A vector X of the form α A + β B ( α and β are numbers) is perpendicular to C . The ratio of α and β is
A force F has magnitude 15N. Direction of F is 37 degrees from negative x axis towards positive y axis. Represent F in terms of i ^ a n d j ^ .
Find the resultant of three vectors OA, OB and OC shown in the following figure. (Radius of the circle is R)
A vector having magnitude 30 unit makes equal angles with each of X, Y and Z-axes. The components of vector along each of X, Y and Z-axes are
If P + Q = Rand IPI = IQI = 3 and IRI = 3, then the angle between P and Q is
If a unit vector is represent by 0 . 5 i ^ + 0 . 8 j ^ + c k ^ then the value of c is
The vector that must be added to the vectors i ^ – 2 j ^ + 3 k ^ and 6 i ^ + 3 j ^ – 7 k ^ so that the resultant vector is a unit vector along the Y-axis is
Which of the following is a vector quantity ?
The angle between two vectors A and B is 120 ∘ , then its resultant C will be
Two forces of 10 N and 8 N act up on a body.The direction of the forces are unknown. The resultant force on the body may be
Unit vector does not have any
Two forces of 10 N and 8N act up on a body .The direction of the forces are unknown . The resultant force on the body may be
The velocities of two bodies A and B are given by u 1 = 10 i ∧ + 30 j ∧ And u 2 = 5 i ∧ − 10 j ∧ . Match the following Column – I Column – II a The magnitude of velocity of A is e 25 units b The magnitude of velocity of B is f 5 65 units c The magnitude of Relative velocity of A with respect to B g 5 5 units d The magnitude of Resultant velocity of A and B is h 10 10 units a b c d 1 h g f e 2 f h e g 3 f e h g 4 g e h f
The velocities of two bodies A and B are given by u 1 = 10 i ^ + 30 j ^ and u 2 = 5 i ^ – 10 j ^ . Match the following Column-I Column-I a) The magnitude of velocity of A is e) 25 units b) The magnitude of velocity of B is f) 5 65 units c) The magnitude of Relative velocity of A with respect to B g) 5 5 units d) The magnitude of Resultant velocity of A and B is h) 10 10 units a b c d 1. h g f e 2. f h e g 3. f e h g 4. g e h f
(N-1) identical forces of magnitude F act simultaneously on a particle each making an angle of 2 π N with the preceding one, the resultant is
One of the two rectangular components of a force is 25N and it makes an angle of 60 0 with the force, the magnitude of the other component is
Two vectors 2 i ^ + 3 j ^ − k ^ and − 4 i ^ − 6 j ^ + λ k ^ are parallel to each other then value of λ will be
Statement A: Addition of vectors obeys Associative law Statement B: subtraction of vectors obeys Distributive law
Length of 2 i ^ + 3 j ^ + 4 k ^ in the xy plane is
The maximum value of the magnitude of the differences of two vectors P and Q can be
When two vectors A and B of magnitudes ‘a’ and ‘b’ respectively are added, the magnitude of resultant vector is always
Statement A : Addition of vectors obeys Associative law Statement B : Subtraction of vectors obeys Distributive law
Two vector 2 i ^ + 3 j ^ − k ^ and − 4 i ^ − 6 j ^ + λ k ^ are parallel to each other then value of λ will be
When two vectors A and B of magnitudes ‘a’ and ‘b’ respectively are added, the magnitude of resultant vector is always
The sum of two vectors A and B is at right. angles to their difference. Then, the correct relation is
The value of λ for which two vectors a = 5 i ^ + λ j ^ + k ^ and b = i ^ – 2 j ^ + k ^ are perpendicular to. each other is
The resultant of two forces has a magnitude 1 N. One of the forces has a magnitude of 3 N and makes an angle of 30 ° with the resultant. The magnitude of the other force is
If a ^ and b ^ are unit vectors and if a ^ × b ^ = 3 a ^ ⋅ b ^ , then the magnitude of the vector ( a ^ − b ^ ) is
The resultant of two forces has a magnitude 1 N. One of the forces has a magnitude of 3 N and makes an angle of 30 ° with the resultant. The magnitude of the other force is
Given that A + B = R and A 2 + B 2 = R 2 . The angle between A and B is
The magnitude of the vector product of two vectors is 3 times their scalar product. The angle between the two vectors is
Given that A ⋅ B = 0 also A x C, = 0. What is the angle between B and C?
A parallelogram is formed with a and b as the sides. Let d 1 and d 2 be the diagonals of the parallelogram. Then a 2 + b 2 = …..
Let F be the force acting on a particle having position vector r and τ the torque of this force about the origin. Then
Given that A + B + C = 0. Two out of the three vectors are equal in magnitude. The magnitude of the third vector is 2 , times that of the either out of the other two. Which of the following can be angle between these vectors ?
The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B, The angle between A and B is
If A = – 2 i ^ + 3 j ^ – 4 k ^ and B = 3 i ^ – 4 j ^ + 5 k ^ , then sinθ = is
The sum of magnitudes of two forces acting at a point is 16 N. If their resultant is normal to the smaller force and has a magnitude of 8 N, then the force are
If the angle between two vectors A and B is θ then the value of the product ( B × A ) . A is equal to
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is
A particle moves so that its position vector is given by r = cos ω t x ^ + sin ω t y ^ , where ω is a constant. Which of the following is true?
If vector A = cosωt i ^ + sinωt j ^ and B = cos ωt 2 i ^ + sin ωt 2 j ^ are functions of time, then the value of t at which they are orthogonal to each other is
A particle moving with velocity v is acted by three forces shown by the vector triangle PQR . The velocity of the particle will
Which of the following vectors is the unit vector along F = − 3 i ^ + 4 j ^ + 12 k ^ N ?
A vector perpendicular to 4 i − 3 j is
Vectors A , B and C are such that A · B = 0 and A · C = 0 Then the vector parallel to A is
If A ¯ = 4 i ^ – 2 j ^ + 6 k ^ , and B ¯ = i ^ – 2 j ^ – 3 k ^ , the angle which the A ¯ + B ¯ makes with the x – axis is
Three vectors satisfy the relation A . B = 0 and A . C = 0. Then A is parallel to
A and B are two vectors given by A = 2 i ^ + 3 j ^ and B = i ^ + j ^ . The magnitude of component of A along B is
Which of the following is a unit vector?
∫ dt 2 at – t 2 = a x sin – 1 [ t a – 1 ] The value of x is
If equation ∫ dt 3 at – 2 t 2 = a x sin – 1 ( t 2 a 2 – 1 ) , the value of x is
Which of the following quantities is dependent of the choice of orientation of the coordinate axes?
If | A + B | = | A | + | B | , then angle between A and B will be
Two vectors A and B lie in a plane, another vector C lies outside this plane, then the resultant of these three vectors i.e., A + B + C
The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force then the forces are
If the sum of two unit vectors is a unit vector, then magnitude of difference is
The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is
The sum of the magnitudes of two forces acting at a point is 16 N. The resultant of these forces is perpendicular to the smaller force and has a magnitude of 8 N. If the smaller force is of magnitude x, then the value of x is
The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90 0 with the force of smaller magnitude, what are the magnitudes of forces ?
Two forces 3 N and 2 N are at an angle θ such that the resultant is R. The first force is now increased to 6 N and the resultant become 2R. The value of θ is
Two forces F 1 = 1 N and F 2 = 2 N act along the lines x = 0 and y = 0 respectively. Then the resultant of forces would be
Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneosuly F 1 = − 4 i ^ − 5 j ^ + 5 k ^ , F 2 = 5 i ^ + 8 j ^ + 6 k ^ , F 3 = − 3 i ^ + 4 j ^ − 7 k ^ and F 4 = 2 i ^ − 3 j ^ − 2 k ^ then the particle will move
A body is at rest under the action of three forces, two of which are F 1 = 4 i ^ , F 2 = 6 j ^ , the third force is
The angle made by the vector A = i ^ + j ^ with x-axis is
With respect to a rectangular cartesian coordinate system, three vectors are expressed as a = 4 i ^ − j ^ , b = − 3 i ^ + 2 j ^ and c = − k ^ where i ^ , j ^ , k ^ are unit vectors, along the X, Y and Z-axis respectively. The unit vector along the direction of sum of these vector is
If A = 3 i ^ + 4 j ^ and B = 7 i ^ + 24 j ^ , the vector having the same magnitude as B and parallel to A is
The unit vector parallel to the resultant of the vectors A = 4 i ^ + 3 j ^ + 6 k ^ and B = − i ^ + 3 j ^ − 8 k ^ is
When A . B = − | A | | B | , then
Let A = i ^ Acosθ + j ^ Asinθ be any vector. Another vector B which is normal to A is
If A and B are perpendicular vectors and vector A = 5 i ^ + 7 j ^ − 3 k ^ and B = 2 i ^ + 2 j ^ − a k ^ . The value of a is
If for two vector A and B , sum ( A + B ) is perpendicular to the difference ( A − B ). The ratio of their magnitude is
The angle between the vectors i ^ + j ^ and ( j ^ + k ^ ) is
The vector P = a i ^ + a j ^ + 3 k ^ and Q = a i ^ − 2 j ^ − k ^ are perpendicular to each other. The positive value of a is
If A = 2 i ^ + 3 j ^ − k ^ and B = − i ^ + 3 j ^ + 4 k ^ then projection of A on B will be
The projection of the vector A = i ^ − 2 j ^ + k ^ on the vector B = 4 i ^ − 4 j ^ + 7 k ^ is
u 1 ^ and u 2 ^ are two unit vectors such that u 1 ^ + u 2 ^ = 2 u 1 ^ − u 2 ^ .Then the angle between u 1 ^ and u 2 ^ is
If A = 2 i ^ + 4 j ^ − 5 k ^ then the direction cosines of the vector A are
The area of the parallelogram represented by the vectors A = 2 i ^ + 3 j ^ and B = i ^ + 4 j ^ is
If for two vectors A and B , A × B = 0 , the vectors
What is the angle between ( P + Q ) and ( P × Q )
What is the unit vector perpendicular to the following vectors 2 i ^ + 2 j ^ − k ^ and 6 i ^ − 3 j ^ + 2 k ^ ?
If A = 5 units, B = 6 units and | A × B | = 15 units , then what is the angle between A and B ?
Three vectors A , B and C satisfy the relation A . B = 0 and A . C = 0 . The vector A is parallel to
If a vector A is parallel to another vector B then the resultant of the vector A × B will be equal to
If A = 3 i ^ + j ^ + 2 k ^ and B = 2 i ^ − 2 j ^ + 4 k ^ then value of | A × B | will be
Which of the following is the unit vector perpendicular to A and B ?
If A × B = B × A then the angle between A and B is
The value of A + B × A − B is
Two adjacent sides of a parallelogram are represented by the two vectors i ^ + 2 j ^ + 3 k ^ and 3 i ^ − 2 j ^ + k ^ . What is the area of parallelogram
If | A × B | = | A . B | , then angle between A and B will be
Vectors A a n d B include an angle θ between them . If ( A + B ) and ( A − B ) respectively subtend angles α and β with A , then ( tanα + tanβ ) is
The position vectors of two balls are given by r 1 = 2 ( m ) i ^ + 7 ( m ) j ^ r 2 = − 2 ( m ) i ^ + 4 ( m ) j ^ What is the distance between the two balls?
A particle whose speed is 50 m/s moves along the line from A(2, 1) to B(9, 25). Find the velocity vector in the form of a i ^ + b j ^
If A × B = C + D , then select the correct alternative .
If unit vectors A ^ and B ^ are inclined at angle θ , then | A ^ − B ^ | is
If A and B are two vectors, which of the following is not correct?
Statement I : A null vector is a vector whose magnitude is zero and direction is arbitrary. Statement II : A null vector does not exist.
Statement I : Two vectors are said to be like vectors if they have same direction but different magnitude. Statement II : Vector quantities do not have specific direction.
Statement I : The minimum number of non-coplanar vectors whose sum can be zero, is four. Statement II : The resultant of two vectors of unequal magnitude can be zero.
Statement I : τ = r ^ × F ^ and τ ≠ F × r Statement II : Cross product of vectors is commutative.
Statement I : Two vectors are said to be equal if, and only if, they have the same magnitude and the same direction. Statement II : Addition and subtraction of scalars make sense only for quantities with same units.
Statement I : The sum of two vectors can be zero. Statement II : The vector cancel each other, when they are equal and opposite.
Statement I : A × B is perpendicular to both A + B as well as A − B Statement II : A + B as well as A − B lie in the plane containing A and B , but A × B lies perpendicular to the plane containing A and B .
Statement I : Angle between i ^ + j ^ and i ^ is 45 0 Statement II : i ^ + j ^ is equally inclined to both i ^ and j ^ and the angle between i ^ and j ^ is 90 0
Statement I : If A . B = B . C , then A may not always be equal to C Statement II : The dot product of two vectors involves cosine of the angle between the two vectors.
Statement I : If dot product and cross product of A and B are zero, it implies that one of the vector A and B must be a null vector. Statement II : Null vector is a vector with zero magnitude.
Statement I : If i and j ^ are unit vectors along x-axis and y-axis respectively, the magnitude of vector i ^ + j ^ will be 2 . Statement II : Unit vector are used to indicate a direction only.
If vectors A = cosωt i ^ + sinωt j ^ and B = cos ωt 2 i ^ + sin ωt 2 j ^ are functions of time, then the value of t at which they are orthogonal to each other is:
Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces? Also name the triangle formed by the forces as sides.
If vectors P, Q and R have magnitude 5, 12 and 13 units and P + Q = R , the angle between Q and R is
Three forces F 1 , F 2 and F 3 are represented as shown. Each of them is of equal magnitude Now match the given columns and select the correct option from the codes given below. Codes
If the resultant of n forces of different magnitudes acting at a point is zero, then the minimum value of n is
Angle between the vectors i ^ + j ^ and j ^ − k ^ is
The angle between the two vectors A = 5 i ^ + 5 j ^ and B = 5 i ^ − 5 j ^ will be
If | A | = 2 and | B | = 4 , then match the relations in Column I with the angle θ between A and B in Column II . Column I Column II (p) | A × B | = 0 (i) θ = 30 0 (q) | A × B | = 8 (ii) θ = 45 0 r | A × B | = 4 (iii) θ = 90 0 (s) | A × B | = 4 2 (iv) θ = 0 0 Mark the correct choice from the given codes. Codes
Six vectors a through f ^ have the magnitudes and directions indicated in the figure. Which of the following statements is true?
Find the resultant of three vectors OA , OB and OC shown in the following figure. Radius of the circle is R.
A scooter going due east at 10 ms – 1 turns right through an angle of 90 0 . If the speed of the scooter remains unchanged in taking turn, the change in the velocity of the scooter is
e ^ r is unit vector along radius of a circle shown in figure . e ^ r can be represented as
A particle P is acted by three coplanar forces as shown in the figure. Find the force needed to prevent the particle P from moving. (take 3 = 1 . 7 )
A person moves 30 m north and then 20 m towards east and finally 30 2 m in south-west direction. The displacement of the person from the origin will be
Weight mg of a block is a force acting downward towards centre of the earth. A block of mass 1 kg is placed on an inclined plane as shown in the figure. Find the x-component and y-component of weight of the block are
Three forces are acting on a particle as shown in the figure. To have the resultant force only along the Y-direction, the magnitude of the minimum additional force needed is
Two horizontal forces of magnitudes 10 N & P N act on a particle. The force of magnitude 10 N acts due west & the force of magnitude P N acts on a hearing of 30 0 east of north as shown in figure. The resultant of these two force acts due north. Find the magnitude of this resultant.
P, Q and R are three coplanar forces acting at a point and are in equilibrium. Given P = 1.9318 kg-wt, sin θ 1 = 0 . 9659 , the value of R is ( in kg – wt )
Five forces 2 N, 3 N , 5 N , 3 and 2 N respectively act at a particle P as shown in the figure . The resultant force on the particle P is
A car going due North at 10 2 ms – 1 turns right through an angle of 90 0 without changing speed. The change in velocity of car is
A force of 5 N acts on a particle along a direction making an angle of 60 0 with vertical. Its vertical component is
A sail boat sails 2 km due East, 5 km 37 0 South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6 km due East, determine the third displacement.
What can be the angle between ( P + Q ) and ( P − Q ) ?
Consider east as positive x-axis, north as positive y-axis. A girl walks 10 m east first time then 10 m in a direction 30 0 west of north for the second time and then third time in unknown direction and magnitude so as to return to her initial position. What is her third displacement in unit vector notation?
A person pushes a box kept on a horizontal surface with force of 100 N. In unit vector notation force can be expressed as :
A truck travelling due north at 20 m/s turns west and travels at the same speed. The change in its velocity be
The magnitude of the x-component of vector A is 3 and the magnitude of vector A is 5. What is the magnitude of the y-component of vector A ?
The component of a vector r along X-axis will have maximum value, if
The x-component of the resultant of several vectors a) is equal to the sum of the x-components of the vectors b) may be smaller than the sum of the magnitudes of the vectors c) may be greater than the sum of the magnitudes of the vectors d) may be equal to the sum of the magitudes of the vectors
Consider the quantities: pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are
Choose the false statement :
Which one of the following statements is true?
The set containing only vector quantities is
Which of the following is meaningful?
Choose the correct statement
The component of a vector is
The resultant of two forces cannot exceed
The minimum number of unequal forces in a plane that can keep a particle in equilibrium is
Given a + b + c + d = 0 which of the following statement is incorrect
If A ⇀ + B ⇀ = R ⇀ and 2 A ⇀ + B ⇀ is perpendicular to B ⇀ then
u ^ 1 and u ^ 2 are two unit vectors such that | u ^ 1 × u ^ 2 | = 3 | u ^ 1 . u ^ 2 | . Then | u ^ 1 + u ^ 2 | is
The condition that they are perpendicular to each other if A = a 1 i ^ + b 1 j ^ and B = a 2 i ^ + b 2 j ^ is
A man can row a boat at a velocity of 10 m/s in still water. Speed of water in the river is 5 m/s. If the man wishes to cross the river in the minimum possible time, the drift produced is [width of river = 1 km]
As x increases from 0 to π 2 the value of sin x:
As θ increases from 0° to 90°, the value of cos θ :
if θ 1 + θ 2 = π 2 and θ 1 = 2 θ 2 ,then value of sin 2 θ 1 + cos 2 θ 2 is :
The greatest value of 5 cos θ -12 sin θ is :
The maximum value of y = sin x cos x is :
Select incorrect alternative.
Sun rays cast 16 m long shadow of a pole, when Sun is 37° above the horizontal. When Sun rises to 53° above the horizontal, length of shadow becomes
A circular arc of length 15 cm has radius 5 cm. The angle subtended by it at centre is :
What is the maximum and minimum values of 3 – cos 2 θ ?
A schematic diagram of a pedestrian overpass is shown in figure. If you walk on the overpass from point A to point B, how far have you walked ?
A 150 cm high girl, when stands 15 m away from a street lamp, light coming from the street lamp cast 3m long shadow of the girl on the horizontal ground. Height of the street lamp above the ground is
If A sin θ = 3 and A cos θ = 4,then select correct alternatives. (i) A = 5 (ii) A = 7 (iii) θ = 37° (iv) θ = 53°
For small ‘ θ ‘ (in radian), select correct alternatives. (i) sin θ =0 (ii) cos θ = 1 (iii) tan θ =0 (iv) tan θ = sin θ
Graph of the function y = 4 + x 2 is shown in figure. What is the value of a?
Graph of an exponential function y = ae -x is shown in figure. What is the value of a?
At points P, Q and R, the values of dy dx and d 2 y dx 2 are given by following expressions (I) At P, dy dx = 0 and d 2 y dx 2 =Negative (II) At Q, dy dx = 0 and d 2 y dx 2 =Positive (Ill) At R, dy dx = 0 and d 2 y dx 2 = zero Select correct alternative :
The shaded area is :
The value of ∫ 1 2 x 2 dx is:
Consider the following statements (A) To convert an angle from degree to radian, we multiply it by π 180 ° (B) The relation between radian and degree is π rad = 180°.
Consider the following statements (A) Slope i . e . , dy dx is positive if y increases with increase in x. (B) Slope of a straight line is a variable quantity. Select the correct options
Consider the following statements (A) Definite integral of a function is defined as the area under the curve. (B) Definite integral of a function is always positive. Select the correct options
For the resultant of two vectors to be maximum, what must be the angle between them?
If A × B = C , then
Find for x: if log(x-1) +log (x+1) = log 2 1
Find the 13th term of the following series: 1,3,5,7,9,11,,,,,,,,
Find the 10th term of the following series: 2,4,8,16,32,64,,,,
Find the sum of the given series for 20 terms: 5+10+15+20+…….
Find the coefficient of x 6 in the expansion of (1 +x) 20
Find the coefficient independent of x in the expansion of (1 +x) 13
The value of sin(270 + θ ) =
The value of ( 1 – cos 2 θ ) cos e c 2 θ
Differentiate sin(3x+5) with respect to x
Differentiate (y-4)(2y + y 2 ) with respect to y
Differentiate y= ( 1 – 8 z ) 1 / 3 with respect to z
Differentiate y= 5 + e 4 t + t 7 with respect to t
Find the integration of cos(3x +5)
Find the integration of 5x+7
Find the integration of 5x+7
Find the integration of 5x+7
Find the angle between the vectors i ^ + j ^ and – j ^
The z component of the resultant of 2 i ^ + 11 j ^ + 13 k ^ and 5 j ^ + 3 k ^ is
A force F has magnitude 15N. Direction of F is 37 degrees from negative x axis towards positive y axis. Represent F in terms of i ^ a n d j ^ .
Find the dot product of A = i ^ + j ^ and B = 2 i ^ – 3 j ^ + 4 k ^
The two vectors A = i ^ – 3 j ^ + y k ^ and B = i ^ + 2 j ^ + x k ^ are perpendicular. Find x y?
The two vectors A = 2 i ^ – 3 j ^ + k ^ and B = i ^ + 2 j ^ + x k ^ are perpendicular. Find x ?
If A = i ^ + 2 j ^ – 3 k ^ and B = j ^ + k ^ are two vectors in space. Then find the cross product of the two vectors
The resultant of two vectors A and B is C . If angle between A and B is θ , then what is the angle between resultant and B
The resultant of two vectors A of magnitude 2 units and B of magnitude 1 unit is C . If angle between A and B is 60 0 , then what is the angle between resultant and B
Vector A = ( 3.0 ± 0.3 ) i and B = ( 4.0 ± 0.4 ) i ^ What is the magnitude of R = A − B ?
A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is
The component of a vector along any other direction is
A vector is added to an equal and opposite vector of similar nature, forms a
Out of the following quantities, which is scalar?
The vector quantity among the following is
Which of the following is a unit vector?
A vector P = 3 i ^ – 2 j ^ + a k ^ is perpendicular to the vector Q = 2 i ^ + j ^ – k ^ . The value of a is
If A = i ^ + j ^ + k ^ and B = – i ^ – j ^ – k ^ , then what is the angle made by ( A – B ) with A ?
The angle between the two vectors – 2 i ^ + 3 j ^ + k ^ and i ^ + 2 j ^ – 4 k ^ is
Component of the vector A = 2 i ^ + 3 j ^ along the vector B = ( i ^ + j ^ ) ) is
Which of the following is the unit vector perpendicular to A and B ?
Condition under which vectors ( a + b ) and ( a – b ) are parallel is
If the angle between two non-zero vectors A and B is 120°, its resultant C will be
The angle between vectors ( A X B ) and ( B x A ) is
What is the angle between (P + Q) and (P X Q)?
If three vectors along coordinate axes represent the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be
The vector that must be added to the vectors i ^ – 2 j ^ + 3 k ^ and 6 i ^ + 3 j ^ – 7 k ^ so that the resultant vector is a unit vector along the Y-axis is
If a unit vector is represent by 0 . 5 i ^ + 0 . 8 j ^ + c k ^ then the value of c is
The resultant of A and B makes an angle α with A and β with B, then
A and B are two vectors given by A = 2 i ^ + 3 j ^ and B = 2 i ^ + 4 j ^ . The magnitude of the’ component of A along B is
Resultant of which of the following may be equal to zero? (a) 10N, 10N, 10N (c) l0N, l0N, 35N (b) 10 N, 10 N, 25 N (d) None of these
Find the resultant of three vectors OA, OB and OC shown in the following figure. (Radius of the circle is R)
If P + Q = Rand IPI = IQI = 3 and IRI = 3, then the angle between P and Q is
The angles which the vector A = 3 i ^ + 6 j ^ + 2 k ^ makes with the coordinate axes are
The component of a vector r along X-axis will have maximum value, if [NCERT Exemplar]
Resultant of two vectors of equal magnitude A is
The direction cosines of vector (A – B), if A = 2 i ^ + 3 j ^ + k ^ , B = 2 i ^ + 2 j ^ + 3 k ^ are
If A = 4 i ^ – 3 j ^ and B = 6 i ^ + 8 j ^ then magnitude and direction of A + B with X-axis will be
If a + b + c = 0, then a X b is equal to
Two vectors A and B are such that A + B = C and A 2 + B 2 = C 2 . If θ is the angle between A and B, then the value of θ is
If vectors A and B have an angle θ between them, then value of | A ^ – B ^ | will be
Given A = 3 i ^ + ∣ 4 j ^ and B = 6 i ^ + 8 j ^ then which of the following option is correct?
The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is
What is the angle between P and the resultant of (P + Q) and (P – Q)?
If a and b are two vectors, then the value of ( a + b ) × ( a – b ) is
Given that A + B = C and that C is perpendicular to A. Further, if |A| = |C|, then what is the angle between A and B?
The resultant of vectors A and B is R 1 . On reversing the direction of vector B, the resultant becomes R 2 . What is the value of R 1 2 + R 2 2 ?
Unit vector perpendicular to vector A = – 3 i ^ – 2 j ^ – 3 k ^ and B = 2 i ^ + 4 j ^ + 6 k ^ both is
The velocity’ of a particle is v ∣ = 6 i ^ + 2 j ^ – 2 k ^ . The component of the velocity parallel to vector a = i ^ + j ^ + k ^ in vector form is
If a i ^ + b j ^ is a unit vector and it is perpendicular to i ^ + j ^ , then value of a and b is
The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the magnitudes of forces?
A vector a is turned without a change in its length through a small angles d θ . The value of ∆ a and ∆ a are, respectively;
Figure shows three vectors p , q and r , where C is the mid-point of AB . Then, which of the following relation is correct?
The angle θ between the vector p = i ^ + j ^ + k ^ and unit vector along X -axis is
In the figure shown, ABCDEF is a regular hexagon. What is the value of AB + AC + AD + AE + AF ?
Which of the following not a vector quantity?
If a vector A having a magnitude of 8 is added to a vector B which lies along X-axis, then the resultant of two vectors lies along Y-axis and has magnitude twice that of B, The magnitude of B is
The value of λ for which two vectors a = 5 i ^ + λ j ^ + k ^ and b = i ^ – 2 j ^ + k ^ are perpendicular to. each other is
The resultant of two forces 1 and P is perpendicular to ‘1’ and equal to 1. What is the value of ‘P’ and angle between the forces
The z component of the resultant of 2 i ^ + 11 j ^ + 13 k ^ and 5 j ^ + 3 k ^ is
The resultant of two vectors A of magnitude 2 units and B of magnitude 1 unit is C . If angle between A and B is 60 0 , then what is the angle between resultant and B
If A = B then which· of the following is not correct?
The forces, which meet at one point but their lines of action do not lie on one plane, are called
A vector is represented by 3 i ^ + j ^ + 2 k ^ . Its length in XY-plane is
Two vectors A and B are such that A + B = C and A 2 + B 2 = C 2 . If θ is the angle between A and B, then the value of θ is
The resultant of two vectors 3P and 2P is R. If the first vector is doubled, then the resultant is also doubled. The angle between the two vectors is
The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is
What is the angle between P and the resultant of (P + Q) and (P – Q)?
The resultant of vectors A and B is R 1 . On reversing the direction of vector B, the resultant becomes R 2 . What is the value of R 1 2 + R 2 2 ?
Three forces 9 N, 12 N and 15 N acting at a point are in equilibrium. The angle between 9 N and 15 N is
Which of the following is a vector quantity ?
Three forces 9 N, 12 N and 15 N acting at a point are in equilibrium the angle between 9 N and 15 N is
A unit vector is represented by 0.5 i ∧ + 0.8 j ∧ + c k ∧ ,then the value of c is
The angle between two vectors A and B is 120 0 , then its resultant C will be
Angle made by a vector 3 i ∧ + 4 j ∧ with Z axis is
Unit vector does not have any
Angle made by a vector 3 i ^ + 4 j ^ with Z axis is
One of the two rectangular components of a force is 25N and it makes an angle of 60 o with the force, the magnitude of the other component is
A = 2 i ^ + 2 j ^ and B = i ∧ + j ∧ then the vector parallel to A and having the magnitude B is
Two equal vectors have a resultant equal to either of them. The angle between them is
A vector 2 i ^ + 2 j ^ rotated about its tail through an angle 45 ∘ in clockwise direction. Then the new vector is
(N-1) identical forces of magnitude F act simultaneously on a particle each making an angle of 2 π N with the preceding one, the resultant is
A = 2 i ^ + 2 j ^ and B = i ^ + j ^ then the vector parallel to A and having the magnitude B is
Find the angle between the vectors i ^ + j ^ and – j ^
If A = i ^ + j ^ + k ^ and B = – i ^ – j ^ – k ^ , then what is the angle made by ( A – B ) with A ?
BC is divided into four equal parts by P, Q and R. The resultant of A B and 3 A C is
Condition under which vectors ( a + b ) and ( a – b ) are parallel is
Component of the vector A = 2 i ^ + 3 j ^ along the vector B = ( i ^ + j ^ ) ) is
Unit vector parallel to the resultant of vector 8 i ^ arid 8 j ^ will be
The angle θ between the vector p = i ^ + j ^ + k ^ and unit vector along X -axis is
What is the angle between (P + Q) and (P X Q)?
If three vectors along coordinate axes represent the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be
A vector a is turned without a change in its length through a small angles d θ . The value of ∆ a and ∆ a are, respectively;
At what angle must the two forces (x + y) and (x – y) act, so that the resultant may be x 2 + y 2 ?
The resultant of A and B makes an angle α with A and β with B, then
If A . B = A X B , then angle between A and B is
A vector perpendicular to both the vectors 2 i ^ – j ^ + 5 k ^ and X-axis is
Vector A ¯ has a magnitude of 3 units and vector B ¯ has a magnitude of 4 units. If the magnitude of A ¯ × B ¯ is 6 units, then the angle between the two vectors is
R is the resultant of two vectors P ¯ and Q ¯ . If R makes an angle of 90 0 with P ¯ and 30 0 with Q ¯ , then the ratio P ¯ : Q ¯ is
Two vectors a and b of different magnitude are found to have a resultant of magnitude R. On reversing one of them, the resultant is again found to have the same magnitude R. Then the angle between the vectors a and b must be
If a ¯ = b ¯ , then which of the following is NOT correct?
If p ¯ , q ¯ and r ¯ are three unit vectors represented by the three sides of an equilateral triangle such that p ¯ ⋅ q ¯ + q ¯ . r ¯ = 0 , then which of the following is the correct relation between the three vectors?
Vector A ¯ has a magnitude of 3 units and vector B ¯ has a magnitude of 4 units. If the magnitude of A ¯ × B ¯ is 6 units, then the angle between the two vectors is
If a ^ and b ^ are unit vectors and if a ^ × b ^ = 3 a ^ ⋅ b ^ , then the magnitude of the vector ( a ^ − b ^ ) is
R is the resultant of two vectors P ¯ and Q ¯ . If R makes an angle of 90 0 with P ¯ and 30 0 with Q ¯ , then the ratio P ¯ : Q ¯ is
Two vectors a and b of different magnitude are found to have a resultant of magnitude R. On reversing one of them, the resultant is again found to have the same magnitude R. Then the angle between the vectors a and b must be
If a ¯ = b ¯ , then which of the following is NOT correct?
Given that A+B=R and A-B=R. The angle between A and B is
Given that A + B = R and A = B = R. what should be the angle between A and B ?
Given that P + Q = R and that R is perpendicular to P. If IPI = IRl, then what is the angle between P and a ?
Given that A + B + C = 0. Out of three vectors two are equal in magnitude and the magnitude of the third vector is 2 times that of either of the two having equal magnitude. Then the angles between vectors are given by
Angle between A x B and B x A is [Figure]
Two billiard balls are rolling on a flat table. One has velocity components v x = 1 m / s , v y = 3 m / s and other has components , v x ′ = 2 m / s and v y ′ = 2 m / s . . If both the balls start moving from the same point, the angle between their Paths is
The diagonals of a parallelogram are 2 i and 2 j. The area of parallelogram is
The radius vector of a point is r = (i – 2 j +3 k) m and a force F = (4 i + 5j) acts at that point. The moment of the force in Nm is
The sum of the magnitudes of two vectors is 18 and the magnitude of their resultant is 12. If the resultant is perpendicular to one of the vectors, then what are the magnitudes of the two vectors ?
The angle between two vectors (i + j) and (j + k) is
The momentum of a particle is p = i 2 cos t + j 2 sin t. what is the angle between the force F acting on the particle and the momentum p ?
what is the torque of the force F=2i-3j+4k. F acting at the point r=3i+ 2j+3k m about origin.
If A=4i-2j+6k and B=i-2j-3k, the angle which the A + B makes with X-axis is
Given that A + B = C and that C is perpendicular to A. Further | A | = | C | then what is the angle between A and B?
The linear velocity of a rotating body is given by v = ω × r where ω is the angular velocity and r is the radius vector. The angular velocity of body ω = i − 2 j + 2 k and their radius vector r = 4i-3k, then | v | is
what is the value of linear velocity of a particle if its angular velocity is ω = 3 i − 4 j + k and i n s tan tan e o u s p o s i t o n v e c t o r i s r = 5 i − 6 j + 6 k ?
The resultant of two forces, one double of the other magnitude, is perpendicular to the smaller of two forces. The angle between the two force is
Three vectors satisfy the relation A . B = 0 and A . C = 0, then A is parallel to
Three forces start acting simultaneously on a particle moving with velocity v. These forces are represented in magnitude and direction by the three sides of a triangle ,ABC (as shown). The particle will now move will velocity
What is the angle between A = 5 ( i ^ – j ^ ) and B = 5 ( i ^ – j ^ ) ?
The angle between the vectors 2i+3j+k and -3i+6k is
