The equations of the lines $l$ and $m$ are
$l: \; \mathbf{r} = a\mathbf{i} + 3\mathbf{j} + b\mathbf{k} + \lambda(c\mathbf{i} - 2\mathbf{j} + 4\mathbf{k})$,
$m: \; \mathbf{r} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k} + \mu(2\mathbf{i} - 3\mathbf{j} + \mathbf{k})$.
Relative to origin $O$, the position vector of $P$ is $4\mathbf{i} + 7\mathbf{j} - 2\mathbf{k}$.
(a)[4]
Given that $l$ is perpendicular to $m$ and that $P$ is on $l$, find the values of the constants $a$, $b$ and $c$.
(b)[6]
The perpendicular from $P$ meets line $m$ at $Q$. Point $R$ is on the extension of $PQ$, with $PQ : QR = 2 : 3$. Find the position vector of $R$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the scalar product of the direction vectors and equate it to zero” …