JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane

x + 2y + 2z = 16

. Let T be a plane passing through the point Q and contains the line

\vec{r} = -\hat{k} + \lambda\left(\hat{i} + \hat{j} + 2\hat{k}\right)

\lambda \in \mathbb{R}

. Then, which of the following points lies on T?

(1) $(2, 1, 0)$
(2) $(1, 2, 1)$ Official answer
(3) $(1, 2, 2)$
(4) $(1, 3, 2)$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Containing a Line and a Point

Same idea in other shifts

Asked 5× in all

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
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
17 Mar 2021, Shift 1 · Q76The equation of the plane which contains the $y$ -axis and passes through the point $(1, 2, 3)$ is :EasySingle correct
17 Mar 2021, Shift 2 · Q77If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.