(i)[2]
Determine the value of $p$ for which $\vec{OA}$ is perpendicular to $\vec{OB}$.
(ii)[4]
Determine the values of $p$ for which the magnitude of $\vec{AB}$ is $7$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
With respect to an origin $O$, the position vectors of the points $A$ and $B$ are $\vec{OA} = \begin{pmatrix}-2 \\ 3 \\ 1\end{pmatrix}$ and $\vec{OB} = \begin{pmatrix}4 \\ 1 \\ p\end{pmatrix}$.