JEE Main 2024 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 1 February 2024, Shift 1, Maths Q30

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

Let the line of the shortest distance between the lines

L_1:\vec{r}=(\hat{i}+2\hat{j}+3\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})

and

L_2:\vec{r}=(4\hat{i}+5\hat{j}+6\hat{k})+\mu(\hat{i}+\hat{j}-\hat{k})

intersect

L_1

and

L_2

at P and Q respectively. If

(\alpha,\beta,\gamma)

is the mid point of the line segment PQ, then

2(\alpha+\beta+\gamma)

is equal to __________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Skew Lines
Idea tested: Equation of Shortest Distance Line

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 108 of the 174 JEE Main shifts held from 2017 to 2026.