3D Geometry PYQs - Last 10 Years
JEE Advanced / Mathematics / Algebra / 18 recent questions
MathematicsAlgebra2017-2026
Practice 18 JEE Advanced Mathematics questions from 3D Geometry. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
18
PYQs on Page
Mathematics / Algebra
2017-2026
Year Range
Based on indexed question metadata
9
Last 5 Years
2022-2026
18
Last 10 Years
2017-2026
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18PYQs
MCQM66.7%
INTEGER16.7%
MCQ16.7%
Difficulty Mix
#1 Medium10
#2 Hard8
9 in last 5 years18 in last 10 years
Last 10 Years 3D Geometry Questions
Showing 18 of 18 filtered questions.
13d Geometry
Let L be the straight line joining the points P(1, 2, –1) and Q(2, 3, 1). Let S be the foot of the perpendicular drawn from the point R(4, –1, 5) to the line L. Another line passing through R intersects L at a point T such that the point S ...
MCQM+4 / -12026
23d Geometry
Let P be the plane such that it contains the straight line $\frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1}$ and is perpendicular to the plane $x+2y+3z=4$. Let $P_1$ be the plane which passes through the point $(4,2,2)$ and is parallel to P.Then ...
MCQM+4 / -12026
33d Geometry
Let $L_1$ be the line of intersection of the planes given by the equations$2x + 3y + z = 4$ and $x + 2y + z = 5$.Let $L_2$ be the line passing through the point $P(2, -1, 3)$ and parallel to $L_1$. Let $M$ denote the plane given by the equa...
MCQM+4 / -22025
43d Geometry
A straight line drawn from the point $P(1,3,2)$, parallel to the line $\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}$, intersects the plane $L_1: x-y+3 z=6$ at the point $Q$. Another straight line which passes through $Q$ and is perpendicular t...
MCQM+4 / -22024
53d Geometry
Let $\gamma \in \mathbb{R}$ be such that the lines $L_1: \frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3}$ and $L_2: \frac{x+16}{3}=\frac{y+11}{2}=\frac{z+4}{\gamma}$ intersect. Let $R_1$ be the point of intersection of $L_1$ and $L_2$. Let $O=...
MCQ+3 / -12024
63d Geometry
Let $\mathbb{R}^3$ denote the three-dimensional space. Take two points $P=(1,2,3)$ and $Q=(4,2,7)$. Let $\operatorname{dist}(X, Y)$ denote the distance between two points $X$ and $Y$ in $\mathbb{R}^3$. Let
$$ \begin{gathered} S=\left\{X \i...
$$ \begin{gathered} S=\left\{X \i...
MCQM+4 / -22024
73d Geometry
Let $\ell_1$ and $\ell_2$ be the lines $\vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k})$ and $\vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k})$, respectively. Let $X$ be the set of all the planes $H$ that contain the line $\ell_1$. For a plane $...
MCQ+3 / -12023
83d Geometry
Let \(S\) be the reflection of a point \(Q\) with respect to the plane given by
\(\vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k}\)
where \(t, p\) are real parameters and \(\hat{\imath}, \hat{\jmath}, \hat{k}\) are the unit vec...
\(\vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k}\)
where \(t, p\) are real parameters and \(\hat{\imath}, \hat{\jmath}, \hat{k}\) are the unit vec...
MCQM+4 / -22022
93d Geometry
Let \(P_{1}\) and \(P_{2}\) be two planes given by
$$ \begin{aligned} &P_{1}: 10 x+15 y+12 z-60=0 \\\\ &P_{2}:-2 x+5 y+4 z-20=0 \end{aligned} $$
Which of the following straight lines can be an edge of some tetrahedron whose two faces lie ...
$$ \begin{aligned} &P_{1}: 10 x+15 y+12 z-60=0 \\\\ &P_{2}:-2 x+5 y+4 z-20=0 \end{aligned} $$
Which of the following straight lines can be an edge of some tetrahedron whose two faces lie ...
MCQM+4 / -22022
103d Geometry
Let \(\alpha\)2 + \(\beta\)2 + \(\gamma\)2 \(\ne\) 0 and \(\alpha\) + \(\gamma\) = 1. Suppose the point (3, 2, \(-\)1) is the mirror image of the point (1, 0, \(-\)1) with respect to the plane \(\alpha\)x + \(\beta\)y + \(\gamma\)...
MCQM+4 / -22020
113d Geometry
Let L1 and L2 be the following straight lines.\({L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}\) and \({L_2}:{{x - 1} \over { - 3}} = {y \over { - 1}} = {{z - 1} \over 1}\).Suppose the straight line $$L:{{x - \alpha } \over ...
MCQM+4 / -22020
123d Geometry
Three lines \({L_1}:r = \lambda \widehat i\), \(\lambda\) \(\in\) R,\({L_2}:r = \widehat k + \mu \widehat j\), \(\mu\) \(\in\) R and \({L_3}:r = \widehat i + \widehat j + v\widehat k\), v \(\in\) R are given.For which point(s) Q on ...
MCQM+4 / -12019
133d Geometry
Let L1 and L2 denote the lines\(r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)\), \(\lambda\)\(\in\) R
and \(r = \mu (2\widehat i - \widehat j + 2\widehat k),\,\mu \in R\) respectively. If L3 is a line which is pe...
and \(r = \mu (2\widehat i - \widehat j + 2\widehat k),\,\mu \in R\) respectively. If L3 is a line which is pe...
MCQM+4 / -12019
143d Geometry
Three lines are given by \(r = \lambda \widehat i,\,\lambda \in R\), \(r = \mu (\widehat i + \widehat j),\,\mu \in R\) and \(r = v(\widehat i + \widehat j + \widehat k),\,v\, \in R\)Let the lines cut the plane x + y + z = 1 at the points ...
INTEGER+3 / -02019
153d Geometry
Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicular to the plane x + y = 3 and the mid-point of PQ lies in the plane x + y = 3) lies on the Z-axis. Let the distance of P ...
INTEGER+3 / -02018
163d Geometry
Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the X-axis, Y-axis and Z-axis, respectively, where O(0, 0, 0) is the origin. Let \(S\left( {{1 \over 2},{1 \over 2},{1 \over 2}} \right)\) be the centre of th...
INTEGER+3 / -02018
173d Geometry
Let P1 : 2x + y \(-\) z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE?
MCQM+4 / -12018
183d Geometry
The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y \(-\) 2z = 5 and 3x \(-\) 6y \(-\) 2z = 7 is
MCQ+3 / -12017