The lines $l$ and $m$ are given by $\mathbf{r} = 2\mathbf{i} - \mathbf{j} + \mathbf{k} + s(2\mathbf{i} + 3\mathbf{j} - \mathbf{k})$ and $\mathbf{r} = \mathbf{i} + 3\mathbf{j} + 4\mathbf{k} + t(\mathbf{i} + 2\mathbf{j} + \mathbf{k})$, respectively.
(i)[4]
Show that these lines are skew.
(ii)[3]
A plane $p$ is parallel to the lines $l$ and $m$. Determine a vector normal to $p$.
(iii)[3]
Given that $p$ is equidistant from the lines $l$ and $m$, determine the equation of $p$. Write your answer in the form $ax + by + cz = d$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set pairs of components equal and solve for $s$ or $t$.” …