(a)[3]
$F$ is located at $(6,1)$, $G$ is located at $(-2,4)$ and $\overrightarrow{GH} = \begin{pmatrix} -1 \\ -8 \end{pmatrix}$. Calculate $|\overrightarrow{FH}|$.
(b(i))[2]
$\overrightarrow{OA} = a$, $\overrightarrow{OB} = b$ and $\overrightarrow{AC} = kb$. $X$ lies on $OC$ such that $OX = m\,OC$. Express $\overrightarrow{OX}$ using $m$, $k$, $a$ and $b$.
(b(ii))[3]
$\overrightarrow{BX} = \frac{3}{5}a - \frac{1}{2}b$. Determine the value of $k$.