If the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{\lambda}$ and $\frac{x-2}{1} = \frac{y-4}{4} = \frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$, then the sum of all possible values of $\lambda$ is:

JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 24 June 2022, Shift 2, Maths Q14

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

If the shortest distance between the lines

\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{\lambda}

and

\frac{x-2}{1} = \frac{y-4}{4} = \frac{z-5}{5}

\frac{1}{\sqrt{3}}

, then the sum of all possible values of

\lambda

is:

(1)16Official answer
(2)6
(3)12
(4)15

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 15× in all

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
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
8 Apr 2024, Shift 2 · Q16If the shortest distance between the lines $\frac{x-\lambda}{2} = \frac{y-4}{3} = \frac{z-3}{4}$ and…MediumSingle correct
9 Apr 2024, Shift 1 · Q16The shortest distance between the lines $\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}$ and $\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}$ is :EasySingle correct
1 Feb 2024, Shift 1 · Q16If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and…MediumSingle correct
27 Jan 2024, Shift 1 · Q18If the shortest distance between the lines $\dfrac{x-4}{1}=\dfrac{y+1}{2}=\dfrac{z}{-3}$ and…MediumSingle correct
30 Jan 2024, Shift 1 · Q28If $d_1$ is the shortest distance between the lines $x+1=2y=-12z$ , $x=y+2=6z-6$ and $d_2$ is the shortest distance between the lines…MediumNumerical value
31 Jan 2024, Shift 2 · Q17The shortest distance, between lines $L_1$ and $L_2$ , where $L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}$ and $L_2$ is the line,…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.