JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2023, Shift 2, Maths Q16

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

Let 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 plane

2x+y-3z=4

. Then the distance of the point

P(1, -9, 2)

from the line L is

(1) $\sqrt{54}$
(2) $\sqrt{69}$
(3) $\sqrt{74}$ Official answer
(4) $9$

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 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
26 Jul 2022, Shift 1 · Q14The length of the perpendicular from the point $(1,\ -2,\ 5)$ on the line passing through $(1,\ 2,\ 4)$ and parallel to the line…MediumSingle 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.