(a)[4]
When $a = 2$, determine the unit vector in the direction of $\overrightarrow{PM}$.
(b)[5]
If $\angle ATP = \cos^{-1}\left(\frac{2}{7}\right)$, determine $a$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
A cuboid $OABCPQRS$ is shown with flat base $OABC$, where $AB = 6\,\text{cm}$ and $OA = a\,\text{cm}$, with $a$ constant. The cuboid has height $OP = 10\,\text{cm}$. Point $T$ lies on $BR$ so that $BT = 8\,\text{cm}$, and $M$ is the mid-point of $AT$. The unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OC$ and $OP$ respectively.