Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts a cuboid $OABCDEFG$ with a horizontal base $OABC$, where $OA = 4$ cm and $AB = 15$ cm. The cuboid has height $2$ cm. Point $X$ lies on $AB$ in such a way that $AX = 5$ cm, and point $P$ lies on $DG$ so that $DP = p$ cm, where $p$ is a constant. Unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OC$ and $OD$ respectively.
(i)[4]
Find the possible values of $p$ so that angle $OPX = 90^\circ$.
(ii)[2]
For the situation when $p = 9$, Find the unit vector in the direction of $\overrightarrow{XP}$.
(iii)[3]
A point $Q$ is on the face $CBFG$ and is such that $XQ$ is parallel to $AG$. Find $\overrightarrow{XQ}$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Writes vector $\overrightarrow{XP}=-4\mathbf{i}+(p-5)\mathbf{j}+2\mathbf{k}$” …