(i)[3]
Determine the values of $p$ for which $\mathbf{u}$ is perpendicular to $\mathbf{v}$.
(ii)[4]
When $p = 1$, determine the angle between the directions of $\mathbf{u}$ and $\mathbf{v}$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The vectors $\mathbf{u}$ and $\mathbf{v}$ are given by $\mathbf{u} = \begin{pmatrix} p^2 \\ -2 \\ 6 \end{pmatrix}$ and $\mathbf{v} = \begin{pmatrix} 2 \\ p - 1 \\ 2p + 1 \end{pmatrix}$, with $p$ as a constant.