3D Geometry PYQs - Last 10 Years

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MathematicsAlgebra2017-2026

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Practice 346 JEE Main Mathematics questions from 3D Geometry. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

346

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Mathematics / Algebra

2017-2026

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228

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346

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346PYQs

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#1 Medium315

#2 Hard20

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Last 10 Years 3D Geometry Questions

Showing 46 of 346 filtered questions.

The plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 and parallel to y-axis
also passes through the point :

If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then :

The equation of the plane containing the straight line \({x \over 2} = {y \over 3} = {z \over 4}\) and perpendicular to the plane containing the straight lines \({x \over 3} = {y \over 4} = {z \over 2}\) and $${x \over 4} = {y \over 2} = {z...

A plane passing through the points (0, –1, 0)
and (0, 0, 1) and making an angle \({\pi \over 4}\) with the
plane y – z + 5 = 0, also passes through the
point

If the line, \({{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 2} \over 4}\) meets the plane,
x + 2y + 3z = 15 at a point P, then the distance of P from the origin is :

Let P be the plane, which contains the line of
intersection of the planes, x + y + z – 6 = 0 and
2x + 3y + z + 5 = 0 and it is perpendicular to the
xy-plane. Then the distance of the point (0, 0, 256)
from P is equal to :

The vertices B and C of a \(\Delta\)ABC lie on the line,
\({{x + 2} \over 3} = {{y - 1} \over 0} = {z \over 4}\) such that BC = 5 units. Then the
area (in sq. units) of this triangle, given that the
point A(1, –1, 2), is :

The equation of a plane containing the line of
intersection of the planes 2x – y – 4 = 0 and
y + 2z – 4 = 0 and passing through the point
(1, 1, 0) is :

The length of the perpendicular from the point
(2, –1, 4) on the straight line,
\({{x + 3} \over {10}}\)= \({{y - 2} \over {-7}}\) = \({{z} \over {1}}\)
is :

The magnitude of the projection of the vector
\(\mathop {2i}\limits^ \wedge + \mathop {3j}\limits^ \wedge + \mathop k\limits^ \wedge\) on the vector perpendicular to the plane
containing the vectors $$\mathop {i}\limits^ \wedge + \m...

The vector equation of the plane through the line
of intersection of the planes x + y + z = 1 and 2x
+ 3y+ 4z = 5 which is perpendicular to the plane
x – y + z = 0 is :

If a point R(4, y, z) lies on the line segment joining
the points P(2, –3, 4) and Q(8, 0, 10), then the
distance of R from the origin is :

The perpendicular distance from the origin to the plane containing the two lines, \({{x + 2} \over 3} = {{y - 2} \over 5} = {{z + 5} \over 7}\) and \({{x - 1} \over 1} = {{y - 4} \over 4} = {{z + 4} \over 7},\) is :

A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is :

If an angle between the line, \({{x + 1} \over 2} = {{y - 2} \over 1} = {{z - 3} \over { - 2}}\) and the plane, \(x - 2y - kz = 3\) is \({\cos ^{ - 1}}\left( {{{2\sqrt 2 } \over 3}} \right),\) then a value of k is :

Let S be the set of all real values of \(\lambda\) such that a plane passing through the points (–\(\lambda\)2, 1, 1), (1, –\(\lambda\)2, 1) and (1, 1, – \(\lambda\)2) also passes through the point (–1, –1, 1). Then S is equal to :

If the line \({{x - 2} \over 3} = {{y + 1} \over 2} = {{z - 1} \over { - 1}}\)
intersects the plane 2x + 3y – z + 13 = 0 at a point P and the plane
3x + y + 4z = 16 at a point Q, then PQ is equal to :

The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines
\(\overrightarrow r = \left( {\widehat i + \widehat j} \right) + \lambda \left( {\widehat i + 2\widehat j - \widehat k} \right)\) and $$\over...

A plane which bisects the angle between the two given planes 2x – y + 2z – 4 = 0 and x + 2y + 2z – 2 = 0,
passes through the point :

The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle \({\pi \over 4}\) with the plane y \(-\) z + 5 = 0 are :

The plane containing the line \({{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z - 1} \over 3}\) and also containing its projection on the plane 2x + 3y \(-\) z = 5, contains which one of the following points ?

If the point (2, \(\alpha\), \(\beta\)) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2\(\alpha\) – 3\(\beta\) is equal to

Two lines \({{x - 3} \over 1} = {{y + 1} \over 3} = {{z - 6} \over { - 1}}\) and \({{x + 5} \over 7} = {{y - 2} \over { - 6}} = {{z - 3} \over 4}\) intersect at the point R. The reflection of R in the xy-plane has coordinates :

The plane passing through the point (4, –1, 2) and parallel to the lines \({{x + 2} \over 3} = {{y - 2} \over { - 1}} = {{z + 1} \over 2}\) and \({{x - 2} \over 1} = {{y - 3} \over 2} = {{z - 4} \over 3}\) also passes through the point -

Let A be a point on the line \(\overrightarrow r = \left( {1 - 3\mu } \right)\widehat i + \left( {\mu - 1} \right)\widehat j + \left( {2 + 5\mu } \right)\widehat k\) and B(3, 2, 6) be a point in the space. Then the value of \(\mu\) for ...

On which of the following lines lies the point of intersection of the line, \({{x - 4} \over 2} = {{y - 5} \over 2} = {{z - 3} \over 1}\) and the plane,
x + y + z = 2 ?

The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles, passes through which one of the following points ?

If Q(0, –1, –3) is the image of the point P in the plane 3x – y + 4z = 2 and R is the point (3, –1, –2), then the
area (in sq. units) of \(\Delta\)PQR is :

If the length of the perpendicular from the point (\(\beta\), 0, \(\beta\)) (\(\beta\) \(\ne\) 0) to the line,
\({x \over 1} = {{y - 1} \over 0} = {{z + 1} \over { - 1}}\) is \(\sqrt {{3 \over 2}}\), then
\(\beta\) is equal to :

If the plane 2x – y + 2z + 3 = 0 has the distances
\({1 \over 3}\)
and
\({2 \over 3}\)
units from the planes 4x – 2y + 4z + \(\lambda\) = 0 and
2x – y + 2z + \(\mu\) = 0, respectively, then the maximum value of \(\lambda\) + \(\mu\) i...

A perpendicular is drawn from a point on the line \({{x - 1} \over 2} = {{y + 1} \over { - 1}} = {z \over 1}\) to the plane x + y + z = 3 such that the
foot of the perpendicular Q also lies on the plane x – y + z = 3. Then the co-ordinates...

If the angle between the lines, \({x \over 2} = {y \over 2} = {z \over 1}\)
and \({{5 - x} \over { - 2}} = {{7y - 14} \over p} = {{z - 3} \over 4}\,\,\) is \({\cos ^{ - 1}}\left( {{2 \over 3}} \right),\) then p is equal to :

The sum of the intercepts on the coordinate axes of the plane passing through the point (\(-\)2, \(-2,\) 2) and containing the line joining the points (1, \(-\)1, 2) and (1, 1, 1) is :

A variable plane passes through a fixed point (3,2,1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz -plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn par...

An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z \(-\) 1 = 0 and 5x + 8y + 2z + 14 =0, is :

An angle between the lines whose direction cosines are gien by the equations,
\(l\) + 3m + 5n = 0 and 5\(l\)m \(-\) 2mn + 6n\(l\) = 0, is :

A plane bisects the line segment joining the points (1, 2, 3) and (\(-\) 3, 4, 5) at rigt angles. Then this plane also passes through the point :

If L1 is the line of intersection of the planes 2x - 2y + 3z - 2 = 0, x - y + z + 1 = 0 and L2 is the line of
intersection of the planes x + 2y - z - 3 = 0, 3x - y + 2z - 1 = 0, then the distance of the origin from the
plane, containing the...

The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane,
x + y + z = 7 is :

If the line, \({{x - 3} \over 1} = {{y + 2} \over { - 1}} = {{z + \lambda } \over { - 2}}\) lies in the plane, 2x−4y+3z=2, then the shortest distance between this line and the line, \({{x - 1} \over {12}} = {y \over 9} = {z \over 4}\) is ...

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate
axes at A, B and C, then the locus of the centroid of \(\Delta\)ABC is :

If x = a, y = b, z = c is a solution of the system of linear equations
x + 8y + 7z = 0
9x + 2y + 3z = 0
x + y + z = 0
such that the point (a, b, c) lies on the plane x + 2y + z = 6, then 2a + b + c equals :

The line of intersection of the planes \(\overrightarrow r .\left( {3\widehat i - \widehat j + \widehat k} \right) = 1\,\,\) and
\(\overrightarrow r .\left( {\widehat i + 4\widehat j - 2\widehat k} \right) = 2,\) is :

The coordinates of the foot of the perpendicular from the point (1, \(-\)2, 1) on the plane containing the lines, \({{x + 1} \over 6} = {{y - 1} \over 7} = {{z - 3} \over 8}\) and $${{x - 1} \over 3} = {{y - 2} \over 5} = {{z - 3} \over 7},...

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line,
\({x \over 1} = {y \over 4} = {z \over 5}\) is Q, then PQ is equal to:

The distance of the point (1, 3, – 7) from the plane passing through the point (1, –1, – 1), having normal
perpendicular to both the lines
\({{x - 1} \over 1} = {{y + 2} \over { - 2}} = {{z - 4} \over 3}\)
and
$${{x - 2} \over 2} = {{y + 1}...