JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 June 2022, Shift 2, Maths Q14

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

If the plane

2x + y - 5z = 0

is rotated about its line of intersection with the plane

3x - y + 4z - 7 = 0

by an angle of

\frac{\pi}{2}

, then the plane after the rotation passes through the point :

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

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Family of Planes Perpendicular to a Third Plane

Same idea in other shifts

Asked 5× in all

8 Apr 2023, Shift 1 · Q15If the equation of the plane containing the line $x+2y+3z-4=0=2x+y-z+5$ and perpendicular to the plane…MediumSingle correct
12 Apr 2023, Shift 1 · Q14Let the plane P: $4x-y+z=10$ be rotated by an angle $\frac{\pi}{2}$ about its line of intersection with the plane $x+y-z=4$ . If $\alpha$ …HardSingle correct
26 Jun 2022, Shift 1 · Q15Let the plane $2x + 3y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3y + 5z = 8$ . If…HardSingle correct
4 Aug 2021, Shift 2 · Q76The distance of the point $(5,6,9)$ from the plane, which passes through the line of intersection of the planes $x+y-z=1$ and…MediumSingle 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.