3.17: Unit vector and point dividing PQ

Find the unit vector in the direction of $40\mathbf{i} - 9\mathbf{j}$.

The position vectors of $P$ and $Q$ relative to $O$ are $\mathbf{p}$ and $\mathbf{q}$. Point $R$ lies on $PQ$ between $P$ and $Q$ such that $\overrightarrow{PR} = k\overrightarrow{PQ}$.

Write down the set of all possible values of $k$.

Given that the position vector of $R$ relative to $O$ is $m\mathbf{p} + n\mathbf{q}$, show that $m + n = 1$.