JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2023, Shift 1, Maths Q14

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

One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along

x

y

and

z

axes are 3, 4 and 5 units respectively. Let P be the vertex

(3,4,5)

. Then the shortest distance between the diagonal OP and an edge parallel to

z

axis, not passing through O or P is:

(1) $\frac{12}{5}$ Official answer
(2) $\frac{12}{5\sqrt5}$
(3) $12\sqrt5$
(4) $\frac{12}{\sqrt5}$

Official answer

Option 1

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Skew Lines
Idea tested: Shortest Distance Between Cube Diagonals

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.