Question

The shortest distance between the lines
$\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}$ is :

• A. $2\sqrt{30}$
• B. $\frac{7}{2}\sqrt{30}$
• C. $3$
• D. $3\sqrt{30}$

Answer 1

Answer: (D)

Shortest distance $=\frac{\Vert \begin{array}{ccc}6& 15& -3\\ 3& -1& 1\\ -3& 2& 4\end{array}\Vert }{\sqrt{11\times 29-49}}=\frac{270}{\sqrt{270}}$
$=\sqrt{270}=3\sqrt{30}$