Consider the lines $L_1: x-1=y-2=z$ and $L_2: x-2=y=z-1$. Let the feet of the perpendiculars from the point $P(5,1,-3)$ on the lines $L_1$ and $L_2$ be $Q$ and $R$ respectively. If the area of the triangle $PQR$ is $A$, then $4A^2$ is equal to :

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q17

Question 17 of 75 in this shift, Maths question 17 of 25, Section A.

Consider the lines

L_1: x-1=y-2=z

and

L_2: x-2=y=z-1

. Let the feet of the perpendiculars from the point

P(5,1,-3)

on the lines

L_1

and

L_2

Q

and

R

respectively. If the area of the triangle

PQR

A

, then

4A^2

is equal to :

(1)139
(2)143
(3)147Official answer
(4)151

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Perpendicular Distance from Point to Line

Same idea in other shifts

Asked 4× in all

5 Apr 2026, Shift 1 · Q13The square of the distance of the point $P(5, 6, 7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to:EasySingle correct
2 Apr 2025, Shift 1 · Q13Let the vertices Q and R of the triangle PQR lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ , $\mathrm{QR}=5$ and the…MediumSingle correct
9 Apr 2024, Shift 2 · Q16Consider the line L passing through the points $(1, 2, 3)$ and $(2, 3, 5)$ . The distance of the point…HardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.