(a) Find the shortest distance between the lines $\frac{x - 8}{3} = \frac{y + 9}{-16} = \frac{z - 10}{7}$ and $\frac{x - 15}{3} = \frac{y - 29}{8} = \frac{z - 5}{-5}$. OR (b) Find the point of intersection of the lines $\vec{r} = \hat{i} - \hat{j} + 6\hat{k} + \lambda$3\hat{i} - \hat{k}$$, and $\vec{r} = -3\hat{j} + 3\hat{k} + \mu$\hat{i} + 2\hat{j} - \hat{k}$$. Also, find the vector equation of the line passing through the point of intersection of the given lines and perpendicular to both the lines.