JEE Main 2026 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 4 April 2026, Shift 2, Maths Q13

Question 13 of 75 in this shift, Maths question 13 of 25, Section A.

The shortest distance between the lines

\vec r=\left(\frac13\hat i+2\hat j+\frac83\hat k\right)+\lambda\left(2\hat i-5\hat j+6\hat k\right)

and

\vec r=\left(-\frac23\hat i-\frac13\hat k\right)+\mu\left(\hat j-\hat k\right)

\lambda,\mu\in\mathbb{R}

, is:

(1) $\sqrt5$
(2)3Official answer
(3) $2\sqrt3$
(4) $\sqrt{15}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Skew Lines
Idea tested: Vector Shortest Distance Formula

Same idea in other shifts

Asked 5× in all

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
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
8 Apr 2024, Shift 1 · Q14If the shortest distance between the lines $L_1:\vec{r}=(2+\lambda)\hat{i}+(1-3\lambda)\hat{j}+(3+4\lambda)\hat{k}$ ,…MediumSingle correct
24 Jun 2022, Shift 1 · Q30If the shortest distance between the lines $\vec{r}=(-\hat{i}+3\hat{k})+\lambda(\hat{i}-a\hat{j})$ and…MediumNumerical value

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.