(a(i))[1]
The point $H$ has coordinates $(5, 2)$, and the point $J$ has coordinates $(-3, 6)$. Find $\vec{HJ}$.
(a(ii))[2]
Calculate the magnitude of $\vec{HJ}$.
(a(iii))[2]
$M$ is the midpoint of $HJ$. Find the position vector of $M$.
(b(i)(a))[1]
The diagram shows a shape built from seven identical equilateral triangles. $\vec{OA} = p$ and $\vec{OF} = q$. Express $\vec{FB}$, as simply as possible, in terms of $p$ and/or $q$.
(b(i)(b))[1]
Express $\vec{FE}$ as simply as possible in terms of $p$ and/or $q$.
(b(ii))[2]
$X$ is a point on $FB$ and $FX : XB = 3 : 1$. Express $\vec{OX}$, as simply as possible, in terms of $p$ and/or $q$.
(b(iii))[3]
$Y$ lies on $BD$. Quadrilateral $OXYF$ is a trapezium. Express $\vec{XY}$, as simply as possible, in terms of $p$ and/or $q$.