(a) Find the shortest distance between the lines $l_1$ and $l_2$ given by : $l_1 : \vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda $4\hat{i} + 6\hat{j} + 12\hat{k}$$ and $l_2 : \vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu $6\hat{i} + 9\hat{j} + 18\hat{k}$$ OR (b) Show that the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z}{1}$ intersect. Also, find their point of intersection.