JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 August 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

The 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

2x+3y+4z=5

, and is perpendicular to the plane

x-y+z=0

(1) $\sqrt{31}$
(2) $2\sqrt{31}$
(3) $\sqrt{62}$ Official answer
(4) $2\sqrt{62}$

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
26 Jun 2022, Shift 2 · Q14If 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…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.