The line $l$ is described by $\mathbf{r} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} + \lambda(2\mathbf{i} - \mathbf{j} + \mathbf{k})$. The plane $p$ is described by $3x + y - 5z = 20$.
(i)[3]
Show that $l$ is contained in $p$.
(ii)[5]
A second plane is parallel to $l$, perpendicular to $p$ and passes through the point with position vector $3\mathbf{i} - \mathbf{j} + 2\mathbf{k}$. Find the equation of this plane, giving your answer in the form $ax + by + cz = d$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Confirm that the point with position vector $\mathbf{i}+2\mathbf{j}-3\mathbf{k}$ lies in the plane” …