The two lines $l$ and $m$ are represented by $\mathbf{r} = 3\mathbf{i} + 2\mathbf{j} + 5\mathbf{k} + s(4\mathbf{i} - \mathbf{j} + 3\mathbf{k})$ and $\mathbf{r} = \mathbf{i} - \mathbf{j} - 2\mathbf{k} + t(-\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$ respectively.
(a)[2]
Show that the lines $l$ and $m$ are perpendicular.
(b)[5]
Show that $l$ and $m$ intersect and state the position vector of their point of intersection.
(c)[4]
Show that the perpendicular distance from the origin to line $m$ is $\frac{1}{3}\sqrt{5}$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the correct procedure to evaluate the scalar product of the relevant vectors” …