Three Dimensional Geometry PYQs - Last 10 Years
WB JEE / Mathematics / Algebra / 23 recent questions
MathematicsAlgebra2017-2026
Practice 23 WB JEE Mathematics questions from Three Dimensional Geometry. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
23
PYQs on Page
Mathematics / Algebra
2017-2026
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Based on indexed question metadata
11
Last 5 Years
2022-2026
23
Last 10 Years
2017-2026
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23PYQs
MCQ95.7%
MCQM4.3%
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#1 Unknown23
11 in last 5 years23 in last 10 years
Last 10 Years Three Dimensional Geometry Questions
Showing 23 of 23 filtered questions.
1Three Dimensional Geometry
The point of intersection of $\vec{r} \times \vec{a}=\vec{b} \times \vec{a}$ and $\vec{r} \times \vec{b}=\vec{a} \times \vec{b}$, where $\vec{a}=\hat{i}+\hat{j}$ and $\vec{b}=2 \hat{i}-\hat{k}$ is
MCQ+1 / -0.252026
2Three Dimensional Geometry
Consider a square $A B C D$ of diagonal length 2a. The square is folded along the diagonal $A C$ so that the plane of $\triangle A B C$ is perpendicular to the plane of $\triangle A D C$. In this case the shortest distance between $A B$ and...
MCQ+1 / -0.252026
3Three Dimensional Geometry
Intercepts of the plane $\vec{r} \cdot \vec{n}=d(\neq 0)$ on the coordinate axes respectively are
MCQ+1 / -0.252026
4Three Dimensional Geometry
The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is
MCQ+1 / -0.252025
5Three Dimensional Geometry
Angle between two diagonals of a cube will be
MCQ+2 / -0.52024
6Three Dimensional Geometry
If the relation between the direction ratios of two lines in \(\mathbb{R}^3\) are given by
\(l+\mathrm{m}+\mathrm{n}=0,2 l \mathrm{~m}+2 \mathrm{mn}-l \mathrm{n}=0\)
then the angle between the lines is
(\(l, \mathrm{~m}, \mathrm{n}\) have t...
\(l+\mathrm{m}+\mathrm{n}=0,2 l \mathrm{~m}+2 \mathrm{mn}-l \mathrm{n}=0\)
then the angle between the lines is
(\(l, \mathrm{~m}, \mathrm{n}\) have t...
MCQ+1 / -0.252024
7Three Dimensional Geometry
The plane \(2 x-y+3 z+5=0\) is rotated through \(90^{\circ}\) about its line of intersection with the plane \(x+y+z=1\). The equation of the plane in new position is
MCQ+1 / -0.252024
8Three Dimensional Geometry
The angle between a normal to the plane \(2x - y + 2z - 1 = 0\) and the X-axis is
MCQ+1 / -0.252023
9Three Dimensional Geometry
If the distance between the plane \(\alpha x - 2y + z = k\) and the plane containing the lines \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}\) and \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) is \(\sqrt 6\), ...
MCQ+1 / -0.252023
10Three Dimensional Geometry
The line \(x - 2y + 4z + 4 = 0\), \(x + y + z - 8 = 0\) intersect the plane \(x - y + 2z + 1 = 0\) at the point
MCQ+1 / -0.252022
11Three Dimensional Geometry
The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y \(-\) z + 4 = 0 and parallel to the x-axis is
MCQ+1 / -0.252022
12Three Dimensional Geometry
A plane meets the co-ordinate axes t the points A, B, C respectively such a way that the centroid of \(\Delta\)ABC is (1, r, r2) for some real r. If the plane passes through the point (5, 5, \(-\)12) then r =
MCQM+2 / -02021
13Three Dimensional Geometry
The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle \(\alpha\). The equation changes to
MCQ+2 / -0.52021
14Three Dimensional Geometry
A line with positive direction cosines passes through the point P(2, \(-\)1, 2) and makes equal angle with co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals.
MCQ+1 / -0.252021
15Three Dimensional Geometry
If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the plane OAB is
MCQ+1 / -0.252021
16Three Dimensional Geometry
The equation of the plane through the point \((2, - 1, - 3)\) and parallel to the lines\({{x - 1} \over 2} = {{y + 2} \over 3} = {z \over { - 4}}\) and \({x \over 2} = {{y - 1} \over { - 3}} = {{z - 2} \over 2}\) is
MCQ+1 / -0.252020
17Three Dimensional Geometry
The sine of the angle between the straight line \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) and the plane \(2x - 2y + z = 5\) is
MCQ+1 / -0.252020
18Three Dimensional Geometry
The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is
MCQ+1 / -0.252019
19Three Dimensional Geometry
The direction ratios of the normal to the plane passing through the points (1, 2, \(-\)3), (\(-\)1, \(-\)2, 1) and parallel to \({{x - 2} \over 2} = {{y + 1} \over 3} = {z \over 4}\) is
MCQ+1 / -0.252019
20Three Dimensional Geometry
A point P lies on a line through Q(1, \(-\)2, 3) and is parallel to the line \({x \over 1} = {y \over 4} = {z \over 5}\). If P lies on the plane 2x + 3y \(-\) 4z + 22 = 0, then segment PQ equals
MCQ+1 / -0.252018
21Three Dimensional Geometry
The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, \(-\)11, 4) and (2, \(-\)3, 1) is
MCQ+1 / -0.252018
22Three Dimensional Geometry
The equation of the plane through (1, 2, \(-\)3) and (2, \(-\)2, 1) and parallel to X-axis is
MCQ+1 / -0.252017
23Three Dimensional Geometry
Three lines are drawn from the origin O with direction cosines proportional to (1, \(-\)1, 1), (2, \(-\)3, 0) and (1, 0, 3). The three lines are
MCQ+1 / -0.252017