Find the shortest distance between the lines whose vector equations are : $\overrightarrow{r}= (\hat i+2 \hat j+3 \hat k)+ \lambda (2 \hat i+ 3 \hat j +4 \hat k)$ and $\overrightarrow{r}= (2 \hat i+4 \hat j+5 \hat k)+ (4 \hat i+ 6 \hat j +8 \hat k)$

Question

$\begin{array}{1 1} \large\frac{\sqrt 5}{\sqrt {29}} \\ \large\frac{\sqrt 3}{\sqrt {29}} \\ \large\frac{\sqrt 7}{\sqrt {29}} \\ \large\frac{\sqrt 5}{\sqrt {27}} \end{array}$