The line $l$ is represented by ${\bf r} = 4\mathbf{i} - \mathbf{j} + 2\mathbf{k} + \lambda(2\mathbf{i} - 3\mathbf{j} + 6\mathbf{k})$. The plane $p$ goes through the point $(4, -1, 2)$ and is at right angles to $l$.
(i)[2]
Find the equation of $p$, giving your answer in the form $ax + by + cz = d$.
(ii)[3]
Find the perpendicular distance from the origin to $p$.
(iii)[3]
A second plane $q$ is parallel to $p$ and the perpendicular distance between $p$ and $q$ is $14$ units. Find the possible equations of $q$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $2x-3y+6z$ as the LHS of equation” …