Find the shortest distance between the lines $\overrightarrow r = ( \hat i + 2\hat j + \hat k) + \lambda ( \hat i - \hat j + \hat k )$ and $\overrightarrow r = 2 \hat i - \hat j - \hat k + \mu (2\hat i + \hat j + 2\hat k )$

Question

This question has appeared in model paper 2012

$\begin{array}{1 1} \large\frac{12}{\sqrt{35}} \\\large\frac{9}{\sqrt {35}} \\\large\frac{4 \sqrt 2}{2} \\ \large\frac{3 \sqrt2}{2} \end{array}$