3.19: Collinear points and resultant of bearing vectors

The position vectors of $P$, $Q$ and $R$ relative to $O$ are $\begin{pmatrix} 4 \\ 7 \end{pmatrix}$, $\begin{pmatrix} 8 \\ 5 \end{pmatrix}$ and $\begin{pmatrix} x \\ y \end{pmatrix}$. Point $R$ lies on $PQ$ extended such that $3\overrightarrow{QR} = 2\overrightarrow{PR}$. Find $x$ and $y$.

Given $\mathbf{a} + \mathbf{b} = \mathbf{c}$, with $|\mathbf{a}| = 5$ on bearing $210^{\circ}$ and $|\mathbf{c}| = 10$ on bearing $330^{\circ}$, find $\mathbf{a}$ and $\mathbf{c}$ in terms of $\mathbf{i}$ and $\mathbf{j}$.

Find the magnitude and bearing of $\mathbf{b}$.