JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2022, Shift 2, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

A plane

E

is perpendicular to the two planes

2x-2y+z=0

and

x-y+2z=4

, and passes through the point

P(1,-1,1)

. If the distance of the plane

E

from the point

Q(a,a,2)

3\sqrt{2}

, then

(PQ)^2

is equal to

(1) $9$
(2) $12$
(3) $21$ Official answer
(4) $33$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Perpendicular to Two Planes

Same idea in other shifts

Asked 4× in all

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
28 Jun 2022, Shift 2 · Q16Let the plane $ax+by+cz=d$ pass through $(2, 3, -5)$ and is perpendicular to the planes $2x+y-5z=10$ and $3x+5y-7z=12$ . If a, b, c, d are…MediumSingle correct
24 Feb 2021, Shift 1 · Q76The equation of the plane passing through the point $(1, 2, -3)$ and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$ ,…EasySingle 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.