Question:

Shortest distance between $\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}$ and $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}$ is

$6\sqrt{3}$

$2\sqrt{6}$

$6\sqrt{2}$

$3\sqrt{6}$

Step-by-Step Solution

Key Concept: $SD=\frac{|\overrightarrow{A_1A_2}\cdot(\vec{d}_1\times\vec{d}_2)|}{|\vec{d}_1\times\vec{d}_2|}$.

$SD=3\sqrt{6}$.

Correct Answer: 4