JEE Main Maths · Three Dimensional Geometry

Planes in 3D in JEE Main

Name: Planes in 3D: JEE Main previous year questions
Creator: Lumi

Planes in 3D (Maths, Three Dimensional Geometry) came 14 times in 10 of the 42 JEE Main shifts Lumi analysed, across 11 distinct ideas. 0 of them came in 2024–26; it was last asked in 2023.

Questions: 14; in 10 shifts
Ideas asked: 11; 3 asked more than once
Numerical answer: 5; 36% of its questions
Pattern: Comes in cycles; rarely asked since 2024

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 9Hard 4

Format

Single correct9 Q
Numerical value5 Q

Ideas inside the topic

11 ideas

Plane Containing a Line and a Point2 Q
Image of a Point in a Plane2 Q
Plane Through Two Points Parallel to a Vector2 Q
Angle Between a Line and a Plane1 Q
Family of Planes1 Q
Intercept Form of Plane1 Q
Direction of Line of Intersection1 Q
Distance Between Parallel Planes1 Q
Perpendicular Bisector Plane1 Q
Plane Perpendicular to Two Planes1 Q
Plane Through Three Points1 Q

Where it sits

Part of Three Dimensional Geometry, which had 84 questions in all. Planes in 3D accounts for 17% of them. In Lumi's JEE taxonomy it belongs to Vectors and 3D Geometry.

Every question

All 14 Planes in 3D questions

Newest first, each with its options and official answer.

6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes $2x-y+z=3$ , $4x-3y+5z+9=0$ and parallel to the line…MediumSingle correct
6 Apr 2023, Shift 1 · Q30Let the image of the point $(1,2,3)$ in the plane $2x-y+z=9$ be Q. If the coordinates of the point R are $(6,10,7)$ , then the square of…MediumNumerical value
8 Apr 2023, Shift 2 · Q13Let $P$ be the plane passing through the line $\frac{x-1}{1} = \frac{y-2}{-3} = \frac{z+5}{7}$ and the point $(2, 4, -3)$ . If the image of…MediumSingle correct
8 Apr 2023, Shift 2 · Q14For $a, b \in \mathbb{Z}$ and $|a - b| \leq 10$ , let the angle between the plane $P: ax + y - z = b$ and the line…HardSingle correct
8 Apr 2023, Shift 2 · Q30Let $P_1$ be the plane $3x - y - 7z = 11$ and $P_2$ be the plane passing through the points $(2, -1, 0)$ , $(2, 0, -1)$ , and $(5, 1, 1)$ .…HardNumerical value
11 Apr 2023, Shift 1 · Q2Let $(\alpha, \beta, \gamma)$ be the image of the point $P(2, 3, 5)$ in the plane $2x + y - 3z = 6$ . Then $\alpha + \beta + \gamma$ is…MediumSingle correct
11 Apr 2023, Shift 1 · Q8If equation of the plane that contains the point $(-2, 3, 5)$ and is perpendicular to each of the planes $2x + 4y + 5z = 8$ and…MediumSingle correct
13 Apr 2023, Shift 2 · Q14The plane, passing through the points $(0,-1,2)$ and $(-1,2,1)$ and parallel to the line passing through $(5,1,-7)$ and $(1,-1,-1)$ , also…MediumSingle correct
25 Jul 2022, Shift 1 · Q14Let $P$ be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing…HardSingle correct
29 Jun 2022, Shift 1 · Q29Let $P_1: \vec{r}\cdot(2\hat{i} + \hat{j} - 3\hat{k}) = 4$ be a plane. Let $P_2$ be another plane which passes through the points…MediumNumerical value
18 Mar 2021, Shift 1 · Q85Let the plane $ax+by+cz+d=0$ bisect the line joining the points $(4,-3,1)$ and $(2,3,-5)$ at the right angles. If a, b, c, d are integers,…EasyNumerical value
9 Jan 2020, Shift 2 · Q74If the distance between the plane, $23x-10y-2z+48=0$ and the plane containing the lines $\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3}$ and…HardNumerical value
2 Sep 2020, Shift 1 · Q66The plane passing through the points $(1, 2, 1)$ , $(2, 1, 2)$ and parallel to the line, $2x=3y$ , $z=1$ also passes through the point :MediumSingle correct
6 Sep 2020, Shift 2 · Q67A plane P meets the coordinate axes at A, B and C respectively. The centroid of $\Delta$ ABC is given to be $(1,1,2)$ . Then the equation of…MediumSingle correct