If y = e kt then d y d t will be
If y = 2 sin 2 θ + tan θ then d y d θ will be
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 f(x) = cos 3 (x 2 ) then find f ‘(x)
Integrate the following : ∫ ( 2 t − 4 ) − 4 d t =
Find the value of tan – 60 °
Draw the graph corresponding to the equation y = – 6 x .
Draw the graph corresponding to the equation y = – 4 x – 6 .
In the equation y = – 4 – 6 e – k t , what is the maximum value of y ?
Find the value of sin – 150 °
Differentiate the following functions with respect to x, x sin x
If a and b are two units vectors inclined at an angle of 60 ° to each other, then
For the figure,
A vector a is turned without a change in its length through a small angle d θ . The value of | Δ a | and ∆ a are respectively
Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be
A car travels 6 km towards north at an angle of 45 o to the east and then travels distance of 4 km towards north at an angle of 135 o to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final position makes with the east?
Find the resultant of three vectors O A , O B and O C shown in the following figure. Radius of the circle is R.
A force is inclined at 60 o to the horizontal. If its rectangular component in the horizontal direction is 50 N, then magnitude of the vertical component of force is approximately
A person pushes a box kept on a horizontal surface with force of 100 N. In unit vector notation force can be expressed as
If a unit vector is represented by 0.5 i ^ + 0.8 j ^ + c k ^ , then the value of ‘c’ is
sin (90º + θ ) is
The maximum value of xy subject to x + y = 8, is :
The area of region between y = sinx and x–axis in the interval 0 , π 2 , will be :
f(x) = tanx then the value of, f π 4
The value of ∫ 0 π / 2 sin 2 x d x will be :
Two vector A and B have equal magnitudes. Then the vector A + B is perpendicular to
What can be the angle between ( P + Q ) and ( P − Q ) ?
If a vector r = x i ^ + y j ^ + z k ^ , makes angle π 3 , π 3 and π n with X-axis, Y-axis and Z-axis respectively. The value of n is .
If a , b and c are non-zero coplanar vectors, such that a ⋅ b = b ⋅ c = 0 . If | a | = 1 unit and | c | = 6 units. The value of | a ⋅ c | . is
Find the value of cos – 60 ° .
For the equation given below, tell the nature of graph. y = – 2 x
Find the value of sec 2 θ – tan 2 θ
For the equation given below, tell the nature of graph. y = 6 e – 4 x
Given, y = 3 x 3 Find the value of d y d t .
Find the maximum/minimum value of y in the functions given below. y = ( sin 2 x – x ) , where – π 2 ≤ x ≤ π 2
Draw straight lines corresponding to following equations. y = 6x – 4
Plot the graph corresponding to the equation x 2 16 + y 2 9 = 1 .
Find 1 + 1 2 + 1 4 + 1 8 + … upto ∞
Find the sum of given geometric series 1+2+4+8+………+256
If the sum of two unit vectors is a unit vector, then find the magnitude of difference of these two vectors
If three vectors along coordinate axis represent the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be
The sum of two forces P and Q is R such that R = P . The angle θ (in degrees) that the resultants of 2 P and Q will make with Q is
A vector A points vertically upward and B points towards north. The vector product A × B is
A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong?
Which pair of the following forces will never give resultant force of 2 N?
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
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 ?
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
If vectors P, Q and R have magnitude 5,12 and 13 units and P + Q = R , the angle between Q and R is
Two forces, each of magnitude F have a resultant of the same magnitude F. The angle between the two forces is
The angle made by the vector A = i ^ + j ^ with x- axis is
Consider a vector F = 4 i ^ − 3 j ^ . Another vector that is perpendicular to F is
A vector is represented by 3 i ^ + j ^ + 2 k ^ . Its length in XY plane is
The component of vector A = 2 i ^ + 3 j ^ along the vector B = i ^ + j ^ is
If a vector P making angles α , β , and γ respectively with the X, Y and Z axes respectively. Then sin 2 α + sin 2 β + sin 2 γ =
If a vector A is parallel to another vector B , then the resultant of the vector A × B will be equal to
cos (A–B) =
y = 1 x + 1 . Find d y d x
Find value of sin 2 15º + sin 2 645º :
sin 2 θ =
If θ = 120º , then
∫ 0 1 t 2 + 9 t + c d t = 9 2 Find the value of ‘c’
Evaluate ∫ − 1 1 x 5 d x
The derivative of f(x) = x 3 + 3x ℓ nx + 5 with respect to x is :
If velocity of particle is given by v = 2t 4 then its acceleration (dv/dt) at any time t will be given by :
If y = x l nx then d y d x will be
What is the angle between P and the resultant of ( P + Q ) and ( P − Q )
If V 1 + V 2 = V 1 − V 2 and V 2 is finite, then
The expression 1 2 i ^ + 1 2 j ^ is a
Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously 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
If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be
The unit vector along i ^ + j ^ is
cos(A+B) =
The value of f”(x) at x = 1 for the function f(x) = x ℓ n x is
If y = 1 x 4 then, d y d x will be :
If y = e x . cot x then d y d x will be
If f(x) = sin 2 x – cos 2 x Then find f ( π /12)
y = 5 sin ( 3 ω t + ϕ ) where ω and ϕ are constant Find d y d t
∫ ( x + 1 ) d y If y = 6 x 2
Value of tan225º is :
Three vectors a , b and c satisfy the relation a ⋅ b = 0 and a ⋅ c = 0 . The vector A is parallel to
Integrate : ∫ 3 2 x d x
Find the volume of parallelepiped (in m 3 ) whose edges are represented by a = ( 2 i ^ − 3 j ^ + 4 k ^ ) m , b = ( i ^ + 2 j ^ − k ^ ) m and c = ( 3 i ^ − j ^ + 2 k ^ ) m .
A force of 1000 N in a particular direction must be applied to a block. For same reason. It is not possible to apply the force in that direction but two forces can be applied to 30 o and 45 o on either side of it in the same plane containing the given force. If the ratio of magnitude of forces as n The value of n is .
In vectors A and B be respectively equal to 3 i ^ − 4 j ^ + 5 k ^ and 2 i ^ + 3 j ^ − 4 k ^ . The unit vector parallel to A + B is 1 27 ( 5 i ^ − a j ^ + k ^ ) The value of a is
If a = 2 i ^ − j ^ + k ^ , b = i ^ + 2 j ^ − 3 k ^ and c = 3 i ^ − y j ^ + 5 k ^ are coplanar. The value of y is
The moon’s distance from the earth is 360000 km and its diameter subtends an angle of 42′ at the eye of the observer. Find the diameter of the moon.
When a clock shows 4 o’clock, how much angle do its minute and hour needles make?
Find the value of sin 240 °
Find the value of cos 120 ° .
Find the value of cosec 2 θ – cot 2 θ – 1
Differentiate the following functions with respect to x, e ( 5 x + 2 )
Differentiate of the following with respect to x . x 2 cos x
Draw the graph corresponding to the equation y = – 2 x + 4 .
The graph shown in figure is exponential. Write down the equation corresponding to the graph.
Differentiate of the following with respect to x . x 4 + 3 x 2 – 2 x
Integrate the following function ∫ π / 6 π / 3 sin x d x
Integrate the following function ∫ 4 10 d x x
The graph shown in figure is exponential. Write down the equation corresponding to the graph.
Draw the following sinusoidal graph y = 2 – 3 cos θ
Draw straight lines corresponding to following equations. y=-6 x
Plot the graphs corresponding to the following equations. y = 4 x
The radius of an air bubble is increasing at the rate of 1 2 cms -1 . Determine the rate of increase in it’s volume when the radius is 1 cm.
Two vectors A and B have magnitudes 6 units and 8 units, respectively. Find |A-B| if the angle between two vectors is 120 °
Two vectors A and B have magnitudes 6 units and 8 units, respectively. Find |A-B| if the angle between two vectors is 90 °
What is the angle between 2 a and 4 a ?
Two vectors have magnitudes 6 units and 8 units, respectively. Find magnitude of resultant of two vectors if angle between two vectors is 0 °
Two vectors have magnitudes 6 units and 8 units, respectively. Find magnitude of resultant of two vectors if angle between two vectors is 120 °
Two vectors of equal magnitudes have a resultant equal to either of them, then the angle between them will be
The sum of magnitudes of two forces is 16 N . If their resultant is normal to the smaller force and has a magnitude of 8 N , then two forces are
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
Unit vector parallel to the resultant of vectors A = 4 i ^ – 3 j ^ and B = 8 i ^ + 8 j ^ will be
If | a + b | | a – b | = 1 , then angle between a and b is
Given that A + B + C = 0 out of three vectors two are equal in magnitude and the magnitude of third vector is 2 times that of either of the two having equal magnitude. Then the angles between vectors are given by
If the sum of two unit vectors is a unit vector, then magnitude of difference 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 o with the force of smaller magnitude, what are the magnitudes of forces?
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
If for two vector A and B , sum ( A + B ) is perpendicular to the difference ( A − B ) . The ratio of their magnitude is
If A × B = C , then which of the following statements is wrong
The magnitudes of vectors A , B and C are 3,4 and 5 units respectively. If A + B = C , the angle between A and B is
In figure, E equals
If P = Q then which of the following is NOT correct
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
In the following options you are given the magnitudes of three forces (in Newton) acting simultaneously on a body. Find the set for which the resultant force on the body can be zero.
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 ?
A force of 6 kg and another of 8 kg can be applied together to produce the effect of a single force of
There are two force vectors, one of 5 N and other of 12N . At what angle the two vectors be added to get resultant vector of 17 N, 7 N and 13 N respectively
Let C = A + B then
When two vectors of magnitudes P and Q are inclined at an angle θ the magnitude of their resultant is 2P. When the inclination is changed to 180 – θ the magnitude of the resultant is halved. Find the ratio of P to Q.
Two forces of magnitudes P and Q are inclined at an angle ( θ ) the magnitude of their resultant is 3Q. When the inclination is changed to (180 – θ ) the magnitude of the resultant force becomes Q. The ratio of the forces P Q is
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 ?
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 unit vector parallel to the resultant of the vectors A = 4 i ^ + 3 j ^ + 6 k ^ and B = − i ^ + 3 j ^ − 8 k ^ is
Angle between the vectors ( i ^ + j ^ ) and ( j ^ − k ^ ) is
Two forces F 1 = 5 i ^ + 10 j ^ − 20 k ^ and F 2 = 10 i ^ − 5 j ^ − 15 k ^ act on a single point. The angle between F 1 and F 2 is nearly
Let A = i ^ A cos θ + j ^ A sin θ be any vector. Another vector B which is normal to A is
The angles which a vector i ^ + j ^ + 2 k ^ makes with X , Y and Z axes respectively are
If P ⋅ Q = P Q , then angle between P and Q is
When A ⋅ B = − | A | | B | then
Vector A makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of A ) will be
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
Which of the following is the unit vector perpendicular to A and B ?
sin(A+B) =
The value of sin(15°) is
The value of sin(75°) is
sin 300º is equal to
If y = x 2 sin x , then d y d x will be
y = 4 + 5 x + 7 x 3 . Find d y d x
If f(x) = x 3 ℓ n (x) Then f ‘(x) is :
If y = x ℓ nx then d y d x will be
Slope of graph y = tanx drawn between y and x, at x = π 4 is :
If y = sin x , then d 2 y d x 2 will be :
sin 750 ∘ =
sin 750 ∘ =
sec ( π + θ ) =
cos 11 π 6 =
If f(x) = sin 3 x – cos(2x), then the value of f π 2 is :
y = sin 3 x, d y d x will be
If α = sec ( 3 β ) then d α d β will be
Differentiation of sin(x 2 ) w.r.t. x is
If y = sin x & x = 3t then d y d t will be
If f ( x ) = sin x , then find f ′ ( x )
∫ 0 1 x − 1 x 2 − 1 d x
Value of ∫ 0 π / 2 cos 3 t d t is
If y = 4cos4x find ∫ y d x
Solve the following Integrals ∫ cos 3 θ 1 − sin θ d θ
Integrate : ∫ 3 2 x d x may be equal to
If y = 3t 2 – 4t ; then minima of y will be at :
If Q = 4v 3 + 3v 2 , then the value of ‘v’ such that, there exist maxima of ‘Q’
∫ x 2 is equal to :
∫ ( x ) 1 / 3 − 1 ( x ) 1 / 3 dx is equal to :
∫ x 3 d x can be equal to :
If y = x 2 sin(x 3 ) then ∫ y dx will be :
∫ 2 sin ( x ) d x is equal to :
The function x 5 – 5x 4 + 5x 3 – 10 has a maxima, when x =
The displacement of a body at any time t after starting is given by s = 15t – 0.4t 2 . The velocity of the body will be 7 ms –1 after time:
If y = x 3 + 2 x 2 + 7 x + 8 then d y d x will be
If y = e x ⋅ cot x then d y d x will be
If y = x 2 sin x , then d y d x will be
y = 4 + 5 x + 7 x 3 . Find d y d x
y = x + x 2 + 1 x + 1 x 3 Find d y d x
The value of ( A + B ) × ( A − B ) is
If the resultant of two forces of magnitude p and 2p is perpendicular to p, then the angle between the forces is
A sail boat sails 2 km due East, 5 km 37 o 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.
A car is moving on a straight road due north with a uniform speed of 50 km h -1 when it turns left through 90 o . If the speed remains unchanged after turning, the change in the velocity of the car in the turning process is
A particle travels with speed 50 m/s from the point (3 m, -7 m) in a direction 7 i ^ − 24 j ^ . Find its position vector after 3 seconds.
How many unit vectors are there for which cos α = 1 2 and cos β = 1 2 , , where α and β are angles made with X-axis and Y-axis, respectively.
Four forces are acting on a particle. one force of magnitude 3 N is directed upward, another is directed 37 o East of North having magnitude 5 N, third is directed in south-west direction is of magnitude 4 2 N and fourth force is 5 n N . If the particle is in equilibrium. The value on n is .
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 o in anti-clockwise direction. Find x-component and y-component in new coordinate system.
If a = 2 i ^ − 3 j ^ + k ^ and b = x i ^ + j ^ + k ^ are mutually perpendicular. The value of x is
Two forces F 1 = ( i ^ + j + k ^ ) N and F 2 = ( i ^ + 2 j ^ + 3 k ^ ) N act on a block and displace it from point A (2,3,4) m to the point B (5,4,3) m. Determine work done (in joule).
The angle between two vectors a = 4 i ^ + 7 j ^ + 6 k ^ and b = 3 i ^ + 3 j ^ − c 10 k ^ is π 3 rad . The value of 3 c 17 is
If a, b and c are non-zero vectors. The value of a ⋅ { ( b + c ) × ( a + b + c ) } is
If c = i ^ × ( a × i ^ ) + j ^ × ( a × j ^ ) + k ^ × ( a × k ^ ) and c = n a . The value of n is
In a circle of radius 4 m, find the angle of an arc of length 1 m subtended at centre.
Which of the following values are positive? (a) cos 120 ° (b) sin 210 ° (c) tan 240 ° (d) cos 315 °
Find the value of cos 120 °
If sin θ = 2 5 then find the value of cos θ and tan θ .
Find the value of cot 300 °
Find the value of tan – 60 °
Find approximate value of tan 3 ° .
For the equation, y = 2 x 2 tell the nature of graph.
A circular arc is of length π cm . Find angle subtended by it at the centre in radian and degree.
Find the value of cos – 60 ° .
Given that sin θ = 1 4 . Find the values of cos θ and tan θ .
Find the value of cos – 60 ° .
Find the value of cos 105 ° + cos 75 ° .
Find the value of tan 105 °
Find the value of 2 sin 15 ° cos 45 °
Find the value of cos 67 ° .
Find the value of 2 sin 45 ° cos 15 °
Differentiate the following functions with respect to x x 3 + 5 x 2 – 2 .
Find the value of sin300° .
Differentiate the following functions with respect to x, x sin x
Differentiate the following functions with respect to x, ( 2 x + 3 ) 6
Find the value of tan210° .
For the equation given below, tell the nature of graph. y = – 2 x
Find d y d x , when y = x 2 + 4 x – 1 / 2 – 3 x – 2
For the equation given below, tell the nature of graph. y = 4 1 – e – 2 x
Find d y d x , when y = x 2 + 4 x – 1 / 2 – 3 x – 2
Find d y d x , when y = x 2 + 4 x – 1 / 2 – 3 x – 2
For the equation y = – 4 x 2 + 6 , find the nature of graph.
Which of the following graphs do not pass through origin? a ) y = 2 x + 6 b ) y 2 – 2 x = 0 c ) y 2 + 3 x 2 + 5 = 0 d ) y + 6 x = 0
Check the quadrants for each part from where the following graph will pass. y = 6 x
Check the quadrants for each part from where the following graph will pass. y = 6 x
If y = x 2 + 2 x 1 / 2 , then find d y d x .
Momentum of a particle is increased by 2% without change in its mass. Find the percentage of change in its kinetic energy.
Find maximum or minimum values of the functions y = 25 x 2 + 5 – 10 x
If y = tan x , find d y d x .
Draw the following sinusoidal graph y = – 3 + 4 sin θ
Differentiate the following with respect to x . x – 1 x
Find maximum or minimum values of the functions y = 9 – ( x – 3 ) 2
If y = x 2 + 3 x + 2 3 + log e x 2 . Then, find d y d x .
Divide a number 100 into two parts such that their product is maximum.
Find the minimum value of y = 5 x 2 – 2 x + 1 .
Differentiate the following with respect to x . 5 x 2 + 6 2 x 2 + 4
Differentiate the following with respect to θ . cos θ ( 1 – sin θ )
Differentiate of the following with respect to x . e x x 5
Differentiate the following the respect to x . x x 2 + 7
Draw the graph corresponding to the equation y = – 6 x .
Differentiate of the following with respect to x . ( 1 + x ) e x
For the graph given below, write down their x , y equation
For the graph given below, write down their x , y equation
Draw the graph corresponding to the equation y = – 4 x – 6 .
Draw the graph corresponding to the equation y = – 2 x + 4 .
For the graph given below, write down their x , y equation
Differentiate with respect to x . ( 6 x + 7 ) 4
For the graph given below, write down their x , y equation
In the equation y = 6 + 4 1 – e – k t , what is the maximum value of y ?
Integrate the following functions with respect to t ∫ 3 t 2 – 2 t d t
Find the maximum/minimum value of y in the functions given below. y = ( sin 2 x – x ) , where – π 2 ≤ x ≤ π 2
Integrate the following functions with respect to t ∫ ( 2 t – 4 ) – 4 d t
Integrate the following functions with respect to t ∫ 4 cos t + t 2 d t
Integrate the following function ∫ 0 2 2 t d t
Integrate the following functions with respect to t ∫ d t ( 6 t – 1 )
Integrate the following function ∫ 1 2 ( 2 t – 4 ) d t
Integrate the following function ∫ 0 π cos x d x
Integrate the following functions with respect to x ∫ ( 6 x + 2 ) 3 d x
Integrate the following functions with respect to x ∫ 4 sin x – 2 x d x
Integrate the following functions with respect to x ∫ d x 4 x + 5
Integrate the following functions with respect to x ∫ ( 6 x + 2 ) 3 d x
Find I = ∫ 0 π / 4 ( sin x + cos x ) d x .
The integral ∫ 1 5 x 2 d x is equal to
Draw straight lines corresponding to following equations. y=2 x
Draw straight lines corresponding to following equations. y = 6x – 4
Plot the graphs corresponding to the following equations. y = 4 x
Plot the graphs corresponding to the following equations. x = 4 y 2 .
Plot the graphs corresponding to the following equations. x 2 + y 2 = 16 .
Velocity of a particle increases exponentially with time from 2 m/s to 6 m/s. Write v-t equation corresponding to it.
Acceleration of a particle decreases exponentially from 10 m / s 2 to 6 m / s 2 . Write a – t equation.
Find the sum of given arithmetic progression 4+8+12+….+64
A man wishes to estimate the distance of a nearby tower from him. He stands at a point A in front of the tower C and spots a very distant object O in line with AC. He then walks perpendicular to AC upto B, a distance of 100 m and looks at O and C again. Since O is very distant, the direction BO is practically the same as AO, but he finds the line of sight of C shifted from the original line of sight by angle θ = 40 0 ( θ i s k n o w n a s p a r a l l a x ) , the distance of tower C from his original position A is
If A = 60 o , then the value of sin ( 2 A ) is equal to
Find dy dx for y = 2 x + x x .
The momentum p of a particle change with time t according to the relation dp dt = 10 + 2 t . If the momentum is zero at t = 0, then the momentum at t = 10 s is
The area of the triangle whose vertices are A (1, -1, 2), B (2, 1, -1) and C (3, -1, 2) is (in area units)
The vector component of 3 i ^ + 4 j ^ along i ^ + j ^ is
If A = 4 i ^ − 3 j ^ and B = 6 i ^ + 8 j ^ then magnitude and direction of A + B will be
In the shown Fig.(b), find the angle between A and B.
In the shown Fig.(a), find the angle between A and B.
What is the angle between a and – 3 2 a .
In the shown Fig, find the angle between A and B.
Two vectors have magnitudes 6 units and 8 units, respectively. Find magnitude of resultant of two vectors if angle between two vectors is 120 °
Two vectors have magnitudes 6 units and 8 units, respectively. Find magnitude of resultant of two vectors if angle between two vectors is 120 °
Two vectors have magnitudes 6 units and 8 units, respectively. Find magnitude of resultant of two vectors if angle between two vectors is 120 °
What is the angle between 3 a and – 5 a ? What is the ratio of magnitude of two vectors?
Two vectors A and B have magnitudes 6 units and 8 units, respectively. Find |A-B| if the angle between two vectors is 120 °
Two vectors A and B have magnitudes 6 units and 8 units, respectively. Find |A-B| if the angle between two vectors is 120 °
Two vectors A and B have magnitudes 6 units and 8 units, respectively. Find |A-B| if the angle between two vectors is 120 °
A vector A points vertically upward and B points towards north. The vector product A × B is
If a and b are two vectors, then the value of ( a + b ) × ( a – b ) is
Let C = A + B
If the vectors ( i ^ + j ^ + k ^ ) and 3 i ^ form two sides of a triangle, the area of the triangle is
If P + Q = R and | P | = | Q | = 3 and | R | = 3 , then the angle betweenP and Q is
Given A = 3 i ^ + 4 j ^ and B = 6 i ^ + 8 j ^ , which of the following statement is correct?
What is the value of ( A + B ) · ( A × B ) ?
If A and B are two vectors such that |A+B|=2|A-B|, the angle between vectors A and B is
Given that P=Q=R. If P+Q=R, then the angle between P and R is θ 1 . If P+Q+R=0, then the angle between P and R is θ 2 . What is the relation between θ 1 and θ 2 ?
A cyclist is moving on a circular path with constant speed v. What is the change in its velocity after it has described an angle of 30 ° ?
If, the resultant of two forces (A + B) and (A – B) is A 2 + B 2 , then the angle between these forces is
If, 0 .5 i ^ + 0 .8 j ^ + c k ^ is a unit vector, then the value of c is
Out of the following set of forces, the resultant of which cannot be zero?
