(a(i))[4]
Find the value of $p$ for which $AB$ and $CB$ have equal lengths.
(a(ii))[4]
For the case $p = 1$, use a scalar product to determine angle $ABC$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The position vectors of $A$, $B$ and $C$ from the origin $O$ are $\vec{OA} = \begin{pmatrix}2\\3\\-4\end{pmatrix}$, $\vec{OB} = \begin{pmatrix}1\\5\\p\end{pmatrix}$ and $\vec{OC} = \begin{pmatrix}5\\0\\2\end{pmatrix}$, with $p$ as a constant.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct vectors are $\vec{AB}=(-1,2,p+4)$ and $\vec{CB}=(-4,5,p-2)$” …
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