If the shortest distance between the lines x-λ/-2=y-2/1=z-1/1 and frac x-√(3) 1 =y-1/-2=z-2/1 is 1 , then the sum of all possible values of λ is :

Mathematics · 3D Geometry

JEE Main 2024 — 1 February, Shift 1 — Question 20

If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and

$\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}$ is 1 , then the sum of all possible values of $\lambda$ is :

Option A:
$0$
Option B:
$2 \sqrt{3}$
Correct
Option C:
$3 \sqrt{3}$
Option D:
$-2 \sqrt{3}$

Answer: B

Step-by-step solution

Passing points of lines $\mathrm{L}_{1} \& \mathrm{~L}_{2}$ are

$(\lambda, 2,1) \&(\sqrt{3}, 1,2)$

S.D $=\frac{\left|\begin{array}{ccc}\sqrt{3}-\lambda & -1 & 1 \\-2 & 1 & 1 \\1 & -2 & 1\end{array}\right|}{\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k}\\ -2 & 1 & 1\\ 1 & -2 & 1\end{array}\right|}$

$1=\left|\frac{\sqrt{3}-\lambda}{\sqrt{3}}\right|$

$\lambda=0, \lambda=2 \sqrt{3}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 1 February, Shift 1
Subject: Mathematics
Chapter: 3D Geometry
Topic: Skew lines & shortest distance between them

Let the line of the shortest distance between the lines L 1: overrightarrow r=(hat i+2 hat j+3 hat k)+lambda(hat i-hat j+hat k) and L 2…

Answer: B

Step-by-step solution

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