(i)[4]
When $ABC$ is a straight line, determine the values of $p$ and $q$.
(ii)[2]
When $\angle BAC=90^\circ$, express $q$ in terms of $p$.
(iii)[3]
When $p = 3$ and the lengths of $AB$ and $AC$ are equal, find the possible values of $q$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
With O as the origin, the position vectors of points A, B and C are given by $\overrightarrow{OA} = \begin{pmatrix}0\\2\\-3\end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix}2\\5\\-2\end{pmatrix}$ and $\overrightarrow{OC} = \begin{pmatrix}3\\p\\q\end{pmatrix}$.
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