The line $l$ is given by $\mathbf{r} = \mathbf{i} + 3\mathbf{j} - 2\mathbf{k} + \lambda(\mathbf{i} - 2\mathbf{j} + 3\mathbf{k})$. The plane $p$ is described by $2x + y - 3z = 5$.
(i)[3]
Find the position vector of the point where $l$ meets $p$.
(ii)[3]
Calculate the acute angle between $l$ and $p$.
(iii)[5]
A second plane $q$ is perpendicular to the plane $p$ and includes the line $l$. Find the equation of $q$, giving your answer in the form $ax + by + cz = d$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write a general point on $l$ in component form” …