Question 8

The position vectors of the points $A, B, C$ and $D$ are $\mathbf{u} = \mathbf{i} + 2\mathbf{j} + \mathbf{k}$, $\mathbf{v} = 7\mathbf{i} + 8\mathbf{j} + 4\mathbf{k}$, $\mathbf{w} = -\mathbf{i} + \mathbf{k}$ and $\mathbf{z} = \mathbf{i} + 2\mathbf{j} + 2\mathbf{k}$ respectively. Show that $\overrightarrow{AB}$ is parallel to $\overrightarrow{CD}$.