(i)[4]
Use a vector approach to work out angle $AOB$.
(ii)[4]
Find the unit vector that points in the direction of $\overrightarrow{OC}$.
(iii)[1]
Show that triangle $OAC$ is an isosceles triangle.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
With $O$ taken as the origin, the position vectors of $A$ and $B$ are $\overrightarrow{OA} = 2\mathbf{i} + 4\mathbf{j} + 4\mathbf{k}$ and $\overrightarrow{OB} = 3\mathbf{i} + \mathbf{j} + 4\mathbf{k}$. Point $C$ is defined so that $\overrightarrow{AB} = \overrightarrow{BC}$.