(i)[3]
Show that $l$ runs parallel to $p$.
(ii)[6]
A line $m$ is contained in plane $p$ and is perpendicular to $l$. It passes through the point with coordinates $(5, 3, 1)$. Find a vector equation for $m$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The vector equation of line $l$ is $\mathbf{r} = \begin{pmatrix}1\\2\\-1\end{pmatrix} + \lambda \begin{pmatrix}2\\1\\3\end{pmatrix}$. The plane $p$ is given by $\mathbf{r} \cdot \begin{pmatrix}2\\-1\\-1\end{pmatrix} = 6$.
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