(i)[3]
Determine the value of $p$ when angle $AOB$ is $90^{\circ}$.
(ii)[4]
When $p = 4$, determine the vector that has magnitude $28$ and lies in the same direction as $\overrightarrow{AB}$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking origin $O$, the position vectors of points $A$ and $B$ are $overrightarrow{OA} = 5\mathbf{i} + \mathbf{j} + 2\mathbf{k}$ and $\overrightarrow{OB} = 2\mathbf{i} + 7\mathbf{j} + p\mathbf{k}$, where $p$ is a constant.