(i)[4]
Find the angle between the vectors $3\mathbf{i} - 4\mathbf{k}$ and $2\mathbf{i} + 3\mathbf{j} - 6\mathbf{k}$.
(ii)[3]
The vector $\overrightarrow{OA}$ has magnitude $15$ units and points in the same direction as $3\mathbf{i} - 4\mathbf{k}$. The vector $\overrightarrow{OB}$ has magnitude $14$ units and points in the same direction as $2\mathbf{i} + 3\mathbf{j} - 6\mathbf{k}$. Express $\overrightarrow{OA}$ and $\overrightarrow{OB}$ in terms of $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(iii)[3]
Find the unit vector that points in the direction of $\overrightarrow{AB}$.