Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts trapezium $OABC$, with $OA$ parallel to $CB$. The position vectors of $A$ and $B$ from the origin $O$ are $\overrightarrow{OA} = \begin{pmatrix} 2 \\ -2 \\ -1 \end{pmatrix}$ and $\overrightarrow{OB} = \begin{pmatrix} 6 \\ 1 \\ 1 \end{pmatrix}$.
(i)[3]
Show that angle $OAB$ is $90^\circ$.
(ii)[3]
The magnitude of $\overrightarrow{CB}$ is three times the magnitude of $\overrightarrow{OA}$. Find the position vector of $C$.
(iii)[3]
Find the exact area of the trapezium $OABC$, giving your answer in the form $a/b$, where $a$ and $b$ are integers.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct vector $\vec{AB}$ or $\vec{BA}$ is found.” …