Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking the origin $O$ as the reference, the position vectors of the points $A$, $B$ and $C$ are $ overrightarrow{OA} = \begin{pmatrix}2 \\ -2 \\ -1\end{pmatrix}$, $ overrightarrow{OB} = \begin{pmatrix}-2 \\ 3 \\ 6\end{pmatrix}$ and $ overrightarrow{OC} = \begin{pmatrix}2 \\ 6 \\ 5\end{pmatrix}$.
(i)[4]
Use a scalar product to determine angle $AOB$.
(ii)[3]
Find the vector that has the same direction as $\overrightarrow{AC}$ and magnitude $15$ units.
(iii)[3]
Find the value of the constant $p$ for which $p\overrightarrow{OA} + \overrightarrow{OC}$ is perpendicular to $\overrightarrow{OB}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies the scalar product formula $\mathbf{a}\cdot\mathbf{b}$.” …