(i)[4]
When $p = 2$, use a scalar product to determine angle $AOB$.
(ii)[4]
When $\overrightarrow{AB}$ is parallel to $\overrightarrow{OC}$, determine $p$ and $q$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Using origin $O$, the position vectors of the points $A$, $B$ and $C$ are $ \overrightarrow{OA} = 3\mathbf{i} + p\mathbf{j} - 2p\mathbf{k}$, $\overrightarrow{OB} = 6\mathbf{i} + (p + 4)\mathbf{j} + 3\mathbf{k}$ and $\overrightarrow{OC} = (p - 1)\mathbf{i} + 2\mathbf{j} + q\mathbf{k}$, with $p$ and $q$ as constants.
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This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Calculates the scalar product $3\times6+2\times6+(-4)\times3=18$” …
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