(a(i))[2]
Calculate the length $|\vec{AB}|$.
(a(ii)(a))[1]
$\vec{AC} = \begin{pmatrix} 6 \\ 2 \end{pmatrix}$ and $C$ is the point $(10, -1)$. Find the coordinates of $A$.
(a(ii)(b))[2]
B is the midpoint of $AD$. Find the coordinates of $D$.
(b(i))[1]
The diagram is triangle $OPQ$. $\vec{OP} = \vec{p}$ and $\vec{OQ} = \vec{q}$. $R$ lies on $OQ$ so that $OR = 2RQ$. $S$ is the midpoint of $PQ$. Express, as simply as possible, in terms of $\vec{p}$ and/or $\vec{q}$, $\vec{PQ}$.
(b(ii))[2]
Express $\vec{OS}$ using $\vec{p}$ and/or $\vec{q}$.
(b(iii))[2]
Express $\vec{SR}$ using $\vec{p}$ and/or $\vec{q}$.