(i)[3]
Find the unit vector pointing in the direction of $\overrightarrow{AB}$.
(ii)[2]
Find the value of the constant $p$ such that angle $BOC = 90^\circ$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
With respect to origin $O$, the position vectors of points $A$, $B$ and $C$ are $\overrightarrow{OA} = \begin{pmatrix}2 \\ -1 \\ 4\end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix}4 \\ 2 \\ -2\end{pmatrix}$ and $\overrightarrow{OC} = \begin{pmatrix}1 \\ 3 \\ p\end{pmatrix}$.