Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

The diagram represents trapezium $ABCD$, with $BA$ parallel to $CD$. Relative to an origin $O$, the position vectors of $A$, $B$ and $C$ are given by $\overrightarrow{OA} = \begin{pmatrix}3\\4\\0\end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix}1\\3\\2\end{pmatrix}$ and $\overrightarrow{OC} = \begin{pmatrix}4\\5\\6\end{pmatrix}$.
(i)[3]

Use a scalar product in order to demonstrate that $AB$ is perpendicular to $BC$.

(ii)[4]

Since the length of $CD$ is $12$ units, determine the position vector of $D$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Employs scalar product $(\mathbf{b}-\mathbf{a})\cdot(\mathbf{b}-\mathbf{c})$” …

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