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BITSAT Three Dimensional Geometry PYQs with Solutions

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

40 questionsMathematics2009–2024Answers + solutions

About Three Dimensional Geometry PYQs

Three Dimensional Geometry has 40 previous year questions in the Quantrex Academy BITSAT Mathematics bank. The 40 questions in this list come from BITSAT (40), spanning 2009 to 2024. Each question opens on its own page with the options, the correct answer and the worked solution where available.

BITSAT Three Dimensional Geometry PYQs with Solutions

About Three Dimensional Geometry PYQs

Questions by year (this list)

Three Dimensional Geometry questions with solutions

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

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 - 2y + 2z - 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 α, β, γ with the coordinate axes. If α + β = (&#960;)/(2) ,~then (cosα + cosβ + cosγ)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 - 2y + z = 0 is p^ 2 then locus of the point is

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

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

If θ is the angle between the vectors 4 ( ^ i - ^ k ) and ^ i + ^ j + ^ k , then (sinθ ++cosθ)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 L_ 1 : x=5, (y)/(3-α)=(z)/(-2)L_ 2 : x=α, y -1 = z 2-α are coplanar. Then, α can take value (s)

A line makes the same angle θ with each of the X and Z -axes. If the angle β , which it makes with Y-axis, is such that ^ 2 β=3 ^ 2 θ, then ^ 2 θ 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 \(π: x-2 y-z=0\). 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

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

Related BITSAT Mathematics chapters

Three Dimensional Geometry in other exams

A line makes angles α, β, γ with the coordinate axes. If α + β = (π)/(2) ,~then (cosα + cosβ + cosγ)2 is equal to

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 is