JEE Main 2023 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 13 April 2023, Shift 2, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

The line, that is coplanar to the line

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

, is

(1) $\frac{x-1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$
(2) $\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$ Official answer
(3) $\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{4}$
(4) $\frac{x+1}{1}=\frac{y-2}{2}=\frac{z-5}{5}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Skew Lines
Idea tested: Coplanarity Determinant Test

Same topic in other shifts

All Skew Lines questions

4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…EasySingle correct
6 Apr 2026, Shift 2 · Q14The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is :EasySingle correct
2 Apr 2025, Shift 2 · Q15The line $L_1$ is parallel to the vector $\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k}$ and passes through the point $(7, 6, 2)$ and the line…EasySingle correct
3 Apr 2025, Shift 1 · Q14Line $\mathrm{L}_1$ passes through the point $(1, 2, 3)$ and is parallel to $z$ -axis. Line $\mathrm{L}_2$ passes through the point…MediumSingle correct
4 Apr 2025, Shift 2 · Q14Let the values of p, for which the shortest distance between the lines $\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5}$ and…MediumSingle correct
7 Apr 2025, Shift 1 · Q14If the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and…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 42 of the 174 JEE Main shifts held from 2017 to 2026.