(a(i))[1]
Point $A$ has position vector $\begin{pmatrix}4\\7\end{pmatrix}$ and point $B$ has position vector $\begin{pmatrix}9\\2\end{pmatrix}$. Determine the column vector $\overrightarrow{AB}$.
(a(ii))[2]
Find $|\overrightarrow{AB}|$.
(a(iii))[2]
$ABCD$ makes up a parallelogram with sides $AB$, $BC$, $CD$ and $DA$. $\overrightarrow{BC} = \begin{pmatrix}-4\\1\end{pmatrix}$. Find the coordinates of point $C$ and point $D$.
(b)[4]
Point $P$ has coordinates $(r,4)$ and point $Q$ has coordinates $(t,u)$. The midpoint of line $PQ$ is $(1,3)$, and the gradient of line $PQ$ is $\frac{1}{4}$. Find the value of each of $r$, $t$ and $u$.