- Let A (1, –1, 3), B (2, 3, 5) is divided by P in the ratio 3:4 internally then harmonic conjugate of P w.r.t. to A, B is
- The co-ordinates of the point where the line through the points A ( 3 , 4 , 1 ) and B ( 5 , 1 , 6 ) crosses the xy-plane
- The point in x y – plane which is equidistant from the points A ( 1 , – 1 , 0 ) , B ( 2 , 1 , 2 ) and C ( 3 , 2 , – 1 )
- The point on z-axis which is equidistant from the points ( 1 , 5 , 7 ) and ( 5 , 1 , – 4 )
- The coordinates of a point which is equidistant from the four points O , A , B and C . When O is the origin and A , B , C are the points on the axes of respectively at distances 2,6,4 from the origin in the positive side is
- The mid points of the sides of a triangle are ( 1 , 5 , − 1 ) , ( 0 , 4 , − 2 ) , ( 2 , 3 , 4 ) . The distance from origin to the farthest vertex from origin is
- The points 2 , 3 , 5 , − 1 , 5 , − 1 , 4 , − 3 , 2 forms
- The equation of the line of intersection of planes 4 x + 4 y − 5 z = 12 and 8 x + 12 y − 13 z = 32 can be written as
- If A = ( 1 , 2 , 3 ) and B ( 3 , 5 , 7 ) and P , Q are the points on A B such that A P = P Q = Q B , then the mid point of PQ is
- If the points ( 5 , 4 , 2 ) , ( 8 , k , − 7 ) and ( 6 , 2 , − 1 ) are collinear, then k =
- If the points A , B , C , D are collinear and C , D divide A B in the ratios 2 : 3 , − 2 : 3 respectively, then the ratio in which A divides C D is
- The points A ( 2 , 9 , 12 ) , B ( 1 , 8 , 8 ) , C ( − 2 , 11 , 8 ) , D ( − 1 , 12 , 12 ) form
- The coordinates of the point which divides lhe line joining the points ( 2 , 3 , 4 ) ind ( 3 , − 4 , 7 ) in the ratio 2 : 4 externally is
- If L,M are the feet of the perpendiculars from ( 2 , 4 , 5 ) to x y -plane and yz-plane respectively, then distance LM is
- In a three dimensional co-ordinate system P,Q and R are images of a point A(a,b,c) in the xy, yz and zx planes respectively. If G is the centroid of triangle PQR then area of triangle AOG is ( O is the origin )
- If A.B.C are projections of P (5,-2,6) on coordinate axes then centriod of △ ABC is
- The ortho centre of triangle formed by the points (2,1,5),(3,2,3), (4,0,4) is
- If x 1 , y 1 , z 1 , x 2 , y 2 , z 2 and x 3 , y 3 , z 3 are the vertices of an equilateral triangle such that x 1 − 2 2 + y 1 − 3 2 + z 1 − 4 2 = x 2 − 2 2 + y 2 − 3 2 + z 2 − 4 2 = x 3 − 2 2 + y 3 − 3 2 + z 3 − 4 2 then ∑ x 1 + 2 ∑ y 1 + 3 ∑ z 1
- If the projections of a line of length d on the coordinate axes are d 1 , d 2 , d 3 respectively, then d 1 2 + d 2 2 + d 3 2 − d 2 =
- The projections of a line segment on the axes are 1,2,2. If the length of the segment is n, then log 3 n =
- If the projections of the line segment A B ¯ on the coordinate planes are 2 , k , 6 and A B = 6 , then k 2 − 7 =
- The projections of the line segment A B ¯ on the axes are 5,12,7. Then the length of A B ¯ is
- Let P = 1 , 2 , 0 , Q = 4 , 0 , − 2 are any two points in the space. Suppose that d 1 , d 2 are the projections of P Q on the x – axis, y z – p l a n e respectively, then d 1 2 – d 2 2
- If α , β are the roots of the quadratic equation x 2 − 5 x + 6 = 0 such that α < β and the vertices of a triangle are A 3 , 5 , − 2 , B α , β , 5 , C − 1 , β , α ,then the triangle is
- If the projections of the line segment A B ¯ on the y z – plane, z x – plane, x y – plane are 160 , 153 and 5 respectively, then the projection of A B ¯ on the z – axis is
- If ( 2 , 3 , 4 ) is the centroid of the tetrahedron for which ( 2 , 3 , − 1 ) , ( 3 , 0 , − 2 ) , ( − 1 , 4 , 3 ) are three vertices , then the distance of the fourth vertex from the origin is
- If A ( 1 , 2 , 3 ) , B ( 2 , 3 , 4 ) and A B is produced up to C such that 2 A B = B C , then C =
- The Locus of a point for which the sum of the squares of the distances from the coordinate axes is 16 units is
- If Q is the image of P ( – 1 , 2 , – 3 ) with respect to the y z – plane then the distance P Q is
- The line passing through the points 5 , 1 , a , 3 , b , 1 crosses the y z – plane at the point 0 , 17 2 , − 13 2 then
- The equation of the line passing through the points 0 , 0 , 0 , 3 , 0 , 0 is
- The number of octants in which both x – and y – coordinates are negative is
- The graph of the equation y 2 + z 2 = 0 in the three – dimensional space is
- If P Q be the projections of 3 , − 2 , 4 on the coordinate planes x y , y z respectively then P Q is
- If the projections of a line segment of length “ d ” on the coordinate axes are d 1 , d 2 , d 3 respectively then d 1 2 + d 2 2 + d 3 2 =
- The coplanar points 3 , 2 , 5 , 2 , 1 , 1 , − 1 , 4 , 1 , 0 , 5 , 5 form a
- The points − 1 , 0 , 1 , 0 , 1 , − 1 , 1 , − 1 , 0 , 2 3 , 2 3 , 2 3 form a
- The point which divides the line segment joining − 3. − 2 , 4 , − 1 , − 4 , 2 in the ratio 3 : 2 internally is
- The line segment joining the points A 2 , 3 , 4 , B − 6 , 5 , − 4 intersect x z – plane at
- If the z-coordinate of a point on the line joining the points B 3 , − 2 , 2 and C 6 , − 17 , − 4 is 0 , Then x-coordinate of the point is
- Let A and B are two given points. Let P divide A B internally and Q divides A B externally in the same ratio. Then A P , A B , A Q are in
- The harmonic conjugate of 2 , 3 , 4 with respect to the points 3 , − 2 , 2 , 6 , − 17 , − 4 is
- If A 2 , 3 , − 1 , B 5 , 6 , 3 , C 2 , − 3 , 1 are the vertices of triangle A B C , the length of the median A D is
- If D 2 , 1 , 0 , E 2 , 0 , 0 , F 0 , 1 , 0 are mid points of the sides B C , C A , A B of triangle A B C respectively. Then, the centroid of triangle A B C is
- Origin is the centroid of the triangle formed by a , 1 , 3 , − 2 , b , − 5 and 4 , 7 , c then ascending order of a , b , c is.
- The points P 1 , 3 , 4 , Q − 1 , 6 , 10 , R − 7 , 4 , 7 and S forms Rhombus then S =
- If the ortho center and the circum center of a triangle are − 3 , 5 , 2 , 6 , 2 , 5 then its centroid is
- The circumcentre of triangle formed by the points 1 , 2 , 3 , 3 , − 1 , 5 , 4 , 0 , − 3 is
- The incentre of the triangle formed by 0 , 0 , 0 , 3 , 0 , 0 , 0 , 4 , 0 is
- If α , β , γ , are the roots of x 3 − 2 x 2 − 5 x + 6 = 0 , the orthocenter of the triangle with vertices α , β , γ , β , γ , α , γ , α , β is
- The distance between the circumcentre and the orthocentre of the triangle formed by 1 , 2 , 3 , 3 , − 1 , 5 , 4 , 0 , − 3 is
- If P , Q , R are the images of A 6 , 3 , 2 with respect to the x – , y – , z – axes respectively, then the distance of the centroid of the triangle P Q R from the origin is
- The x , y , z coordinates of each vertex of a triangle are in geometric progression .The x and y coordinates of the centroid of the triangle are 1 and 2 respectively. The distance of the centroid from the origin is.
- Let A ( 3 , 2 , 0 ) , B ( 5 , 3 , 2 ) , C ( − 9 , 6 , − 3 ) are three points forming a triangle. If A D , the bisector of ∠ B A C meets B C in D , then coordinates of D are
- If the point x 1 + t x 2 − x 1 , y 1 + t y 2 − y 1 , z 1 + z 2 − z 1 devides the line segment joining x 1 , y 1 , z 1 ) and x 2 , y 2 , z 2 internally then
- A triangle ABC is placed so that the mid-points of the sides are on the x,y,z axes. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively α , β , γ . Coordinates of the centroid of the triangle ABC are
- G ( 1 , 1 , − 2 ) is the centroid of the triangle ABC and D is the mid point of BC . If A = ( − 1 , 1 , − 4 ) then D =
- α , β , γ are the root of x 3 − 2 x 2 − x + 2 = 0 . Centroid of triangle with verties α , β , γ , ( β , γ , α ) , ( γ , α , β )
- If a △ A B C the mid points of the sides A B , B C , C A are respectively ( l , 0 , 0 ) , ( 0 , m , 0 ) and ( 0 , 0 , n ) then A B 2 + B C 2 + C A 2 l 2 + m 2 + n 2 =
- In △ A B C if A B = 2 , A C = 20 , B = ( 3 , 2 , 0 ) and C = ( 0 , 1 , 4 ) then the length of the median passing through A is
- A ( 5 , 4 , 6 ) , B ( 1 , − 1 , 3 ) and C ( 4 , 3 , 2 ) form △ A B C . If the internal bisector of angle A meets B C in D , then the length of A D ¯ is
- The distance between the origin and the centroid of the tetrahedron whose vertices are (0,0,0), (a,0,0), (0,b,0), (0,0,c) is
- If ( Cos α , sin α , 0 ) , ( cos β , sin β , 0 ) , ( cos γ , sin γ , 0 ) are vertices of a triangle then circum radius R is
- A ( 0 , 2 , 3 ) , B ( 2 , − 1 , 5 ) , C ( 3 , 0 , − 3 ) are vertices of △ A B C . If a , b , c are HG, GS, SH then their increasing order is ( H , G , S are orthocentre, centroid and circumcentre)
- A plane is parallel to yz-plane so it is perpendicular to
- ln which of the following point lies in a fourth octant? (1 , 2, 3) , (4, -2 ,3) , (4 ,-2 ,-5) and (4 ,2, – 5)
- Find the coordinates of a point on Y-axis which are at a distance of 5 2 from the point P(3, – 2,5).
- which of the following pairs of points have a distance 43 ?
- The equation of the set of points which are equidistant from the points (1,2,3) and (3,2, – 1) is
- A point R with x-coordinate 4 lies on the line segment joining the points P(2, – 3, 4) and Q(8, 0, 10). Find the coordinates of the point R
- lf there are three points A(2,3, 4), B(- 1,2, – 3) and C(-4,1, – 10) in a space, then they are
- A plane is parallel xy-plane, so it is perpendicular to
- The locus of a point for which y = 0, z = 0 is
- The point ( – 2, – 3, – 4) lies in the
- Z is the foot of the perpendicular drawn from a point R(3, 4,5) on the xy -plane. The coordinates of point L are
- The distance of point I(3, 4,5) from the yz-plane is
- What is the length of foot of perpendicular drawn from the point P (3, 4,5) on Y-axis?
- If the distance between the points ( α ,0,1) and (0, 1,2) is 27 , then the value of α is
- It A and B be the points (3, 4,5) and (- 1, 3, – 7) respectively, find the equation of the set of points P such that (PA) 2 + (PB) 2 = K 2 , where K is a constant.
- Distance of the point (1,2,3) from the coordinate axes are
- If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is
- The coordinates of a point which is equidistant from the points (0, 0, 0), (o, 0, 0), (0, b, 0), (0,0, c) are given by
- If x 2 + y 2 = 1 then the distance from the point x , y , 1 − x 2 − y 2 to the origin is
- If a parallelepiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelepiped is
- The points A(5, – 1, 1) B(7, – 4,7),C(1, – 6, 10) and D(1 – 3,4) are vertices of a
- The points (5, – 4,2),(4,- 3, 1),(7, – 6, 4) and (8, – 7 , 5) are the vertices of
- If the coordinates of the vertices of a ∆ ABC are A(- 1, 3, 2), B(2, 3, 5) and C(9, b, – 2), then ∠ A is equal to
- Three vertices of a parallelogram ABCD are A(1,2,3), B(- 1, – 2, – 1) and C(2,3,2). Find the fourth vertex D.
- Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1, – 4,6) in the ratio 2 : 3 externally.
- Find the ratio in which the yz-plane divides the line segment formed by joining the points (- 2, 4,7) and (3, – 5, 8).
- Find the length of the medians of the triangle with vertices A(0, 0,6),B(0, 4,0) and C(6,0,0).
- Find the coordinates of the points which trisect the line segment joining the points P(4,2, – 6) and Q(10, – 16,6).
- Find the centroid of a triangle, the mid-point of whose sides are D(1,2, – 3), E(3, 0, 1) and F(- 1,1, – 4).
- The mid-points of the sides of a triangle are (5,7 ,11), (0, 8, 5) and (2,3, – 1). Then, the vertices are
- The area of the triangle, whose vertices are at the points (2, 1, 1), (3, 1,2) and (- 4,0, 1) is
- If vertices of a triangle are A(1,- 1, Z), B(2,0,- 1) and C(0,2,1), then the area of a triangle is
- The triangle formed by the points (0,7,10), (- 1,6,6), (- 4,9,6) is
- The points (5,2,4),(6,- 1,2) and (8, – 7, k) are collinear, if k is equal to
- The point A(1, – 1, 3), B(2, – 4,8) and C(5,- 18, 11) are
- The projections of a line segment on x , y and z axes are respectively 3, 4 and 12. The length of the line segment is
- A line makes an angle of 60 ° with each of x and y axis, the which it makes with z axis is ( in degrees)
- A line A B in three dimensional space makes angles 45 ° and 120 ° with the positive x-axis and positive y-axis respectively. If A B makes an acute angle θ with the positive z-axis, then θ equals ( in degrees)
- P (0, 5, 6), Q (1, 4, 7), R (2, 3, 7) and S (3, 4, 6) are four points in the space. The point farthest from the origin O (0, 0, 0) is