Question

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 sum of possible values of $\lambda$ is

• A. 16
• B. 11
• C. 12
• D. 15

Hint:

Geometry Tip: The shortest distance between skew lines formula $d = \frac{|[\vec{a_2}-\vec{a_1}, \vec{b_1}, \vec{b_2}]|}{|\vec{b_1} \times \vec{b_2}|}$ is purely derived from projecting the displacement vector between the lines onto their mutually perpendicular normal vector.

Answer 1

The Correct Option is A