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Three Dimensional Geometry — BITSAT Mathematics PYQs

40 previous year questions from Three Dimensional Geometry with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

Three Dimensional Geometry — BITSAT Mathematics PYQs

The magnitude of projection of line joining (3,4 , 5) and (4,6,3) on the line joining (-1,2,4) and (1,0,5) is

The angle between the lines whose direction cosines are given by the equations 3 l+m+5 n=0,6 ~nm -2 n l+5 l m =0 is

Let the acute angle bisector of the two planes x-2 y-2 z+1=0 and 2 x-3 y-6 z+1=0 be the plane P . Then which of the following points lies on P?

Let the foot of perpendicular from a point P (1,2,-1) to the straight line L : x 1 = y 0 = z -1 be N . Let a line be drawn from P parallel to the plane x+y+2 z=0 which meets L at p

If the co-ordinates of the point in which the line joining the points (3,5,-7) and (-2,1,8) is intersected by the plane y z is [ a , 13 ~b , c ] , then (a+b-c)=

If the straight lines x-1 k = y-2 2 = z-3 3 and x-2 3 = y-3 k = z-1 2 intersect at a point, then the integer k is equal to

The shortest distance between the lines x = y +2=6 z-6 and x+1=2 y=-12 z is

The ratio in which the YZ-plane divide the line segment formed by joining the points (-2,4,7) and (3,-5,8) is 2: m . The value of m is

The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar if

The shortest distance between the lines x-3 2 = y-2 3 = z-1 -1 and x+3 2 = y-6 1 = z-5 3 is :

If the plane 3 x+y+2 z+6=0 is parallel to the line 3 x-1 2 b =3-y= z-1 a , then the value of 3 a+3 b is

The length of the perpendicular drawn from the point (3,-1,11) to the line x 2 = y-2 3 = z-3 4 is :

A line makes angles of 45^ and 60^ with the positive axes of X and Y respectively. The angle made by the same line with the positive axis of Z , is

The distance from the point (3,4,5) to the point where the line x-3 1 = y-4 2 = z-5 2 meets the plane x+y+z=17 is

The equation of plane containing line x - y = 1 , z = 1 and parallel to x 2 - z 3 = 1 , y = 3 is

The angle between the lines whose direction cosine satisfy the equations l + m + n = 0 and l 2 = m 2 + n 2 is

An equation of plane parallel to plane x - 2 y + 2 z - 5 = 0 and at a unit distance from the origin is

Reflection of the line x - 1 - 1 = y - 2 3 = z - 4 1 in the plane x + y + z = 7 is

A line makes angles &#945; , &#946; , &#947; with the coordinate axes. If &#945; + &#946; = &#960; 2 , then cos &#945; + cos &#946; + cos &#947; 2 is equal to

If the sum of squares of distances of a point from the planes x + y + z = 0 , x - z = 0 and x - 2 y + z = 0 is p 2 then locus of the point is

Line x + 1 &#955; = y - 1 = z + 2 - 4 is perpendicular to 2 x + 2 y - 8 z + 5 = 0 , then &#955; is

If the planes r &#8594; &#183; 2 i ^ - &#955; j ^ + 3 k ^ = 0 and r &#8594; &#183; &#955; i ^ + 5 j ^ - k ^ = 5 are perpendicular to each other, then the value of &#955; 2 + &#955;

If &#952; is the angle between the vectors 4 i ^ - k ^ and i ^ + j ^ + k ^ , then sin &#952; + cos &#952; equals to

The length of perpendicular drawn from the point ( 2 , 3 , 4 ) to line 4 - x 2 = y 6 = 1 - z 3 , is

The image of the point ( 1 , 6 , 3 ) in the line x 1 = y - 1 2 = z - 2 3 is

The distances of the point ( 1 , - 5 , 9 ) from the plane x + y + z = 5 measured along a straight line x = y = z is 2 3 k , then the value of k is

Two lines L₁: x=5, y 3- = z -2 L ₂: x = , y -1 = z 2- are coplanar. Then, can take value (s)

A line makes the same angle with each of the X and Z -axes. If the angle , which it makes with Y-axis, is such that ² =3 ² , then ² equals

Find the angle between the line x+1 2 = y 3 = z-3 6 and the plane 10 x +2 y -11 z =3

The equation of the right bisector plane of the segment joining (2,3,4) and (6,7,8) is

The coordinates of the point where the line through the points A (3,4,1) and B (5,1,6) crosses the XY-plane are

Find the angle between the two planes 2 x + y -2 z =5 and 3 x-6 y-2 z=7

What is the value of n so that the angle between the lines having direction ratios (1,1,1) and (1,-1, n) is 60^ ?

The foot of the perpendicular from the point (7,14,5) to the plane 2 x +4 y - z =2 are

Find the coordinates of the point where the line joining the points (2,-3,1) and (3,-4,-5) cuts the plane 2 x+y+z=7

Gives the line (L: x-1 3 = y+1 2 = z-3 -1 ) and the plane ( : x-2 y-z=0 ). Of the following assertions, the only one that is always true is

If the middle points of sides ( BC , CA ~ &~ AB ) of triangle (A B C ) are respectively (D, E, F ) then position vector of centre of triangle ( DEF ), when position vector of (A, B

The perpendicular distance of (P(1,2,3) ) from the line ( x-6 3 = y-7 2 = z-7 -2 ) is

Solution of the differential equation ( d y d x + y x = x ) is

If the line ( x-4 1 = y-2 1 = z-k 2 ) lies in the plane (2 x-4 y+z=7 ), then the value of (k ) is

A line makes angles α , β , γ with the coordinate axes. If α + β = π 2 , then cos α + cos β + cos γ 2 is equal to

Line x + 1 λ = y - 1 = z + 2 - 4 is perpendicular to 2 x + 2 y - 8 z + 5 = 0 , then λ is

If the planes r → · 2 i ^ - λ j ^ + 3 k ^ = 0 and r → · λ i ^ + 5 j ^ - k ^ = 5 are perpendicular to each other, then the value of λ 2 + λ

If θ is the angle between the vectors 4 i ^ - k ^ and i ^ + j ^ + k ^ , then sin θ + cos θ equals to