JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 29 June 2022, Shift 1, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let

d

be the distance between the foot of perpendiculars of the points

P(1, 2, -1)

and

Q(2, -1, 3)

on the plane

-x + y + z = 1

. Then

d^2

is equal to ____________.

Official answer

NTA final key (2022 Session 1).

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Foot of Perpendicular

Same idea in other shifts

Asked 5× in all

10 Apr 2023, Shift 2 · Q29Let the foot of perpendicular from the point A $(4, 3, 1)$ on the plane P : $x - y + 2z + 3 = 0$ be N. If B $(5, \alpha, \beta)$ ,…HardNumerical value
28 Jul 2022, Shift 1 · Q16The foot of the perpendicular from a point on the circle $x^2+y^2=1,\ z=0$ to the plane $2x+3y+z=6$ lies on which one of the following…HardSingle correct
29 Jul 2022, Shift 2 · Q14Let $Q$ be the foot of perpendicular drawn from the point $P\,(1, 2, 3)$ to the plane $x+2y+z=14$ . If $R$ is a point on the plane such…MediumSingle correct
26 Aug 2021, Shift 2 · Q89Let Q be the foot of the perpendicular from the point $\mathrm{P}(7,-2,13)$ on the plane containing the lines…HardNumerical value

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.