Points $A$ and $B$ are represented by the position vectors $2\mathbf{i} - 3\mathbf{j} + 2\mathbf{k}$ and $5\mathbf{i} - 2\mathbf{j} + \mathbf{k}$ respectively, and plane $p$ is given by $x + y = 5$.
(i)[4]
Determine the position vector of the point where the line through $A$ and $B$ meets the plane $p$.
(ii)[7]
A second plane $q$ is given by $x + by + cz = d$, where $b$, $c$ and $d$ are constants. Plane $q$ contains the line $AB$, and the acute angle between planes $p$ and $q$ is $60^\circ$. Determine the equation of $q$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use a correct procedure to obtain a vector equation for $AB$” …