(i)[3]
Find the cosine value of angle $AOB$.
(ii)[4]
Since $AB$ and $OC$ are equal in length, determine the possible values of $k$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Measured from the origin $O$, the position vectors of points $A$ and $B$ are $
\overrightarrow{OA} = \begin{pmatrix}3 \\ 0 \\ -4\end{pmatrix}$ and $\overrightarrow{OB} = \begin{pmatrix}6 \\ -3 \\ 2\end{pmatrix}$. The position vector of $C$ is $\overrightarrow{OC} = \begin{pmatrix}k \\ -2k \\ 2k - 3\end{pmatrix}$.