(a)[4]
Find the equation of $\Pi$, and give your answer in the form $ax + by + cz = d$.
(b)[5]
The line through $P$, parallel to the $x$-axis, intersects $\Pi$ at the point $B$. Find the distance $AB$, correct to 3 significant figures.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The points $P$ and $Q$ are specified by position vectors, measured from the origin $O$, as $\overrightarrow{OP} = 7\mathbf{i} + 7\mathbf{j} - 5\mathbf{k}$ and $\overrightarrow{OQ} = -5\mathbf{i} + \mathbf{j} + \mathbf{k}$. Point $A$ is the midpoint of $PQ$. Plane $\Pi$ is perpendicular to the line $PQ$ and goes through $A$.