(a) Find the foot of the perpendicular from the point $(0, 2, 3)$ on the line $\frac{-x - 3}{-5} = \frac{1 - y}{-2} = \frac{3z + 12}{9}$ and hence find the length of the perpendicular. OR (b) Find the value of p if the shortest distance between the lines $\vec{r} = $\hat{i} + 2\hat{j} + \hat{k}$ + \lambda $\hat{i} - \hat{j} + \hat{k}$$ and $\vec{r} = $p\hat{i} - \hat{j} - \hat{k}$ + \mu $2\hat{i} + \hat{j} + 2\hat{k}$$ is $\frac{3}{\sqrt{2}}$ units.