JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 24 June 2022, Shift 1, Maths Q30

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

If the shortest distance between the lines

\vec{r}=(-\hat{i}+3\hat{k})+\lambda(\hat{i}-a\hat{j})

and

\vec{r}=(-\hat{j}+2\hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})

\sqrt{\frac{2}{3}}

, then the integral value of a is equal to ______.

Official answer

NTA final key (2022 Session 1).

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

Same idea in other shifts

Asked 9× in all

4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…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
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
4 Apr 2024, Shift 1 · Q29If the shortest distance between the lines $\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}$ and $\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}$ is…HardNumerical value
6 Apr 2024, Shift 1 · Q17The shortest distance between the lines $\frac{x-3}{2}=\frac{y+15}{-7}=\frac{z-9}{5}$ and $\frac{x+1}{2}=\frac{y-1}{1}=\frac{z-9}{-3}$ isMediumSingle 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
25 Jun 2022, Shift 2 · Q30Let $l_1$ be the line in $xy$ -plane with $x$ and $y$ intercepts $\frac{1}{8}$ and $\frac{1}{4\sqrt{2}}$ respectively, and $l_2$ be the…HardNumerical value
24 Feb 2021, Shift 2 · Q88Let $\lambda$ be an integer. If the shortest distance between the lines $x-\lambda=2y-1=-2z$ and $x=y+2\lambda=z-\lambda$ is…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 108 of the 174 JEE Main shifts held from 2017 to 2026.