2.8: Column vectors and a point dividing a segment

Vectors $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ are such that $\mathbf{a} = \begin{pmatrix} 5 \\ -6 \end{pmatrix}$, $\mathbf{b} = \begin{pmatrix} 11 \\ -15 \end{pmatrix}$ and $3\mathbf{a} + \mathbf{c} = \mathbf{b}$.

Find $\mathbf{c}$.

Find the unit vector in the direction of $\mathbf{b}$.

In the diagram, $\overrightarrow{OP} = \mathbf{p}$ and $\overrightarrow{OQ} = \mathbf{q}$. The point $R$ lies on $PQ$ such that $PR = 3RQ$. Find $\overrightarrow{OR}$ in terms of $\mathbf{p}$ and $\mathbf{q}$, simplifying your answer.