The plane given by the equation $2x + 2y - z = 5$ is labelled $m$. Relative to the origin $O$, the coordinates of $A$ and $B$ are $(3, 4, 0)$ and $(-1, 0, 2)$ respectively.
(i)[5]
Show that plane $m$ passes through the midpoint of $AB$ and is perpendicular to $AB$.
(ii)[3]
A second plane $p$ is parallel to $m$ and closer to $O$. The perpendicular separation between the two planes is $1$. Determine the equation of $p$, 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: “State or obtain the midpoint coordinates $(1,2,1)$ for $AB$” …