The planes $p$ and $q$ are defined by the equations $x + y + 3z = 8$ and $2x - 2y + z = 3$, respectively.
(i)[4]
Calculate the acute angle between the planes $p$ and $q$.
(ii)[7]
Point $A$ on the line of intersection of $p$ and $q$ has $y$-coordinate $2$. Find the equation of the plane that passes through $A$ and is perpendicular to both planes $p$ and $q$. Give 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: “Give or suggest a correct normal vector to either plane, for example $\mathbf{i}+\mathbf{j}+3\mathbf{k}$ or $2\mathbf{i}-2\mathbf{j}+\mathbf{k}$” …