The equation of the line $l$ is $\mathbf{r} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k} + u(2\mathbf{i} - \mathbf{j} - 2\mathbf{k})$.
(i)[5]
The point $P$ is given by the position vector $4\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}$. Determine the perpendicular distance from $P$ to $l$.
(ii)[6]
It is stated that $l$ lies in the plane with equation $ax + by + 2z = 13$, where $a$ and $b$ are constants. Determine the values of $a$ and $b$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write $\overrightarrow{PQ}$ for any point $Q$ on $l$, for instance $-3\mathbf{i}+6\mathbf{k}+\mu(2\mathbf{i}-\mathbf{j}-2\mathbf{k})$” …