Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking $O$ as the origin, the position vectors of the three points $A$, $B$ and $C$ are $\vec{OA} = \mathbf{i} + 2p\mathbf{j} + q\mathbf{k}$, $\vec{OB} = q\mathbf{i} - 2p\mathbf{k}$ and $\vec{OC} = -(4p^2 + q^2)\mathbf{i} + 2p\mathbf{j} + q\mathbf{k}$, where $p$ and $q$ are constants.
(i)[2]
Show that $\vec{OA}$ and $\vec{OC}$ are perpendicular for every non-zero pair of values of $p$ and $q$.
(ii)[2]
Determine the magnitude of $\vec{CA}$ in terms of $p$ and $q$.
(iii)[3]
For the values $p = 3$ and $q = 2$, find the unit vector parallel to $\vec{BA}$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme.