(a)[3]
$\vec{PQ} = \begin{pmatrix}5\\-8\end{pmatrix}$.\n(i) Determine $|\vec{PQ}|$.\n(ii) Given that $Q$ is the point $(2,-3)$, determine the coordinates of $P$.
(b)[6]
In the diagram, $M$ is the midpoint of $AB$ and $L$ is the midpoint of $OM$. Also, $ON=\frac{1}{3}OB$. Let $OA=\vec{a}$ and $OB=\vec{b}$.\n(i) Determine $\vec{OM}$, $\vec{OL}$ and $\vec{AL}$.\n(ii) Determine the ratio $AL:AN$.
(c)[5]
Triangle $A$ is displayed on a grid.\n(i) Draw its image under the transformation represented by $\begin{pmatrix}-1.5 & 0\\0 & -1.5\end{pmatrix}$.\n(ii) Determine the $2\times2$ matrix that sends triangle $A$ to triangle $B$.