JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q14

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

The length of the perpendicular from the point

(1,\ -2,\ 5)

on the line passing through

(1,\ 2,\ 4)

and parallel to the line

x + y - z = 0 = x - 2y + 3z - 5

is :

(1) $\sqrt{\frac{21}{2}}$ Official answer
(2) $\sqrt{\frac{9}{2}}$
(3) $\sqrt{\frac{73}{2}}$
(4) $1$

Official answer

Option 1

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 9× 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
7 Apr 2025, Shift 2 · Q17Consider 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 $L_1$ …MediumSingle correct
4 Apr 2024, Shift 2 · Q16Let P be the point of intersection of the lines $\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}$ and…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
6 Apr 2023, Shift 2 · Q16Let the line L pass through the point $(0, 1, 2)$ , intersect the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and be parallel to the…HardSingle correct
30 Jun 2022, Shift 1 · Q28Consider a triangle ABC whose vertices are $A(0, \alpha, \alpha)$ , $B(\alpha, 0, \alpha)$ and $C(\alpha, \alpha, 0)$ , $\alpha > 0$ . Let D…HardNumerical value
31 Aug 2021, Shift 2 · Q74The distance of the point $(-1, 2, -2)$ from the line of intersection of the planes $2x+3y+2z = 0$ and $x-2y+z = 0$ is :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.