(a) Show that the area of a parallelogram whose diagonals are represented by $\vec{a}$ and $\vec{b}$ is given by $\frac{1}{2} |\vec{a} \times \vec{b}|$. Also find the area of a parallelogram whose diagonals are $2\hat{i} - \hat{j} + \hat{k}$ and $\hat{i} + 3\hat{j} - \hat{k}$. OR (b) Find the equation of a line in vector and cartesian form which passes through the point $(1, 2, -4)$ and is perpendicular to the lines $\frac{x - 8}{3} = \frac{y + 19}{-16} = \frac{z - 10}{7}$, and $\vec{r} = 15\hat{i} + 29\hat{j} + 5\hat{k} + \mu$3\hat{i} + 8\hat{j} - 5\hat{k}$$.