(i)[3]
Find the values of $p$ that make angle $AOB$ equal to $90^\circ$.
(ii)[3]
When $p = 3$, find the unit vector pointing in the direction of $\overrightarrow{BA}$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Using origin $O$ as the reference point, the position vectors for points $A$ and $B$ are $\overrightarrow{OA} = \begin{pmatrix}3p\\4\\p^2\end{pmatrix}$ and $\overrightarrow{OB} = \begin{pmatrix}-p\\-1\\p^2\end{pmatrix}$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate dot product or scalar product condition $\overrightarrow{OA}\cdot\overrightarrow{OB}=0$” …
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