Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The points $O$, $A$ and $B$ are given by $\overrightarrow{OA} = \mathbf{i} + 3\mathbf{j} + p\mathbf{k}$ and $\overrightarrow{OB} = -7\mathbf{i} + (1 - p)\mathbf{j} + p\mathbf{k}$, with $p$ as a constant.
(i)[3]
Find the values of $p$ such that $\overrightarrow{OA}$ is perpendicular to $\overrightarrow{OB}$.
(ii)[2]
The lengths of $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are $a$ and $b$ respectively. Find the value of $p$ for which $b^2 = 2a^2$.
(iii)[3]
Find the unit vector in the direction of $\overrightarrow{AB}$ when $p = -8$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate use of the scalar product $\vec{OA} \cdot \vec{OB}$.” …