(i)[4]
Find the angle $AOB$.
(ii)[1]
Find $\vec{BC}$ expressed in terms of $p$ and vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(iii)[4]
Find the value of $p$, given that $BC$ is perpendicular to $OA$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The figure depicts triangle $OAB$, where the position vectors of $A$ and $B$ relative to $O$ are $\vec{OA} = 2\mathbf{i} + \mathbf{j} - 3\mathbf{k}$ and $\vec{OB} = -3\mathbf{i} + 2\mathbf{j} - 4\mathbf{k}$. $C$ lies on $OA$ such that $\vec{OC} = p\vec{OA}$, with $p$ a constant.