(i)[3]
Determine the value of $a$.
(ii)[6]
The line given by $\mathbf{r} = \mathbf{j} - \mathbf{k} + \lambda(\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$ meets plane $p$ at $A$ and plane $q$ at $B$. Determine the length of $AB$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Plane $p$ is given by $3x + 2y + 4z = 13$. A further plane $q$, with equation $ax + y + z = 4$, is perpendicular to $p$, where $a$ is a constant.