Review question

# Which point $P$ is on both this line and this plane? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6006

## Question

The line $l$ has the equation $\mathbf{r}= \begin{pmatrix}5\\ 0\\ 5\end{pmatrix}+ \lambda \begin{pmatrix}2\\ 1\\ 0\end{pmatrix}, \hspace{1cm} \lambda \in \mathbb{R}.$

1. Show that $l$ lies in the plane whose equation is $\mathbf{r}.\begin{pmatrix}-1\\ 2\\ 0\end{pmatrix}=-5.$
2. Find the position vector of $L$, the foot of the perpendicular from the origin $O$ to $l$.
3. Find an equation of the plane containing $O$ and $l$.
4. Find the position vector of the point $P$ where $l$ meets the plane $\pi$ whose equation is $\mathbf{r}.\begin{pmatrix}1\\ 2\\ 2\end{pmatrix} = 11.$