(a) Find the shortest distance between the lines: $\frac{x+1}{2} = \frac{y-1}{1} = \frac{z-9}{-3}$ and $\frac{x-3}{2} = \frac{y+15}{-7} = \frac{z-9}{5}$. OR (b) Find the image $A'$ of the point $A(2, 1, 2)$ in the line $l: \vec{r} = 4\hat{i} + 2\hat{j} + 2\hat{k} + \lambda $\hat{i} - \hat{j} - \hat{k}$$. Also, find the equation of line joining $AA'$. Find the foot of perpendicular from point $A$ on the line $l$.