Find the distance between the lines:

$$\begin{aligned} & \vec{r}=(\hat{i}+2 \hat{j}-4 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) ; \\ & \vec{r}=(3 \hat{i}+3 \hat{j}-5 \hat{k})+\mu(4 \hat{i}+6 \hat{j}+12 \hat{k}) \end{aligned}$$