Mathematics - Vector Question with Solution | TestHub

If the shortest distance between the lines $\begin{array}{ll}{L}_1:\vec{r}=(2+\lambda )\hat{i}+(1-3\lambda )\hat{j}+(3+4\lambda )\hat{k},& \lambda \in \mathbb{R}\\ L_2:\vec{r}=2(1+\mu )\hat{i}+3(1+\mu )\hat{j}+(5+\mu )\hat{k},\mu \in \mathbb{R}& \end{array}$ is $\frac{m}{\sqrt{n}}$, where $\gcd (m,n)=1$, then the value of $m+n$ equals