JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 August 2021, Shift 2, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

Let Q be the foot of the perpendicular from the point

\mathrm{P}(7,-2,13)

on the plane containing the lines

\frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8}

and

\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-3}{7}

. Then

(\mathrm{PQ})^2

, is equal to __________.

Official answer

NTA final key.

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
29 Jun 2022, Shift 1 · Q23Let $d$ be the distance between the foot of perpendiculars of the points $P(1, 2, -1)$ and $Q(2, -1, 3)$ on the plane $-x + y + z = 1$ .…MediumNumerical 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.