Taking O as the origin, the vector equations of lines $l$ and $m$ are $\mathbf{r} = 2\mathbf{i} + \mathbf{k} + \lambda(\mathbf{i} - \mathbf{j} + 2\mathbf{k})$ and $\mathbf{r} = 2\mathbf{j} + 6\mathbf{k} + \mu(\mathbf{i} + 2\mathbf{j} - 2\mathbf{k})$ respectively.
(i)[4]
Prove that lines $l$ and $m$ do not intersect.
(ii)[3]
Calculate the acute angle formed by the directions of $l$ and $m$.
(iii)[5]
Find the equation of the plane that is parallel to $l$ and contains $m$, giving your answer in the form $ax + by + cz = d$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write a general point on $l$ or $m$ in component form” …