The shortest distance between the lines $I_1$ and $I_2$ given by

$I_1: \vec{r}=\hat{i} + 2\hat{j}-4\hat{k}+ \lambda (2\hat{i} + 3\hat{j} + 6\hat{k} ) $ and $I_2 : \vec{r}=3\hat{i}+3\hat{j}-5\hat{k} + \mu (2\hat{i} + 3\hat{j}+6\hat{k})$ is :

$\frac{\sqrt{293}}{7}$