(i)[3]
Find the position vector of $P$.
(ii)[1]
Find the distance $OP$.
(iii)[2]
Determine whether $OP$ is perpendicular to $AB$. Justify your answer.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking $O$ as the origin, the position vectors of $A$ and $B$ are $\overrightarrow{OA} = \begin{pmatrix}5\\1\\-2\end{pmatrix}$ and $\overrightarrow{OB} = \begin{pmatrix}5\\4\\-3\end{pmatrix}$. The point $P$ is on $AB$ and satisfies $\overrightarrow{AP} = \frac{1}{3}\overrightarrow{AB}$.
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct vector $\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$” …
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