The line \(l\) has the equation \[\mathbf{r}= \begin{pmatrix}5\\ 0\\ 5\end{pmatrix}+ \lambda \begin{pmatrix}2\\ 1\\ 0\end{pmatrix}, \hspace{1cm} \lambda \in \mathbb{R}.\]
- Show that \(l\) lies in the plane whose equation is \[\mathbf{r}.\begin{pmatrix}-1\\ 2\\ 0\end{pmatrix}=-5.\]
- Find the position vector of \(L\), the foot of the perpendicular from the origin \(O\) to \(l\).
- Find an equation of the plane containing \(O\) and \(l\).
- Find the position vector of the point \(P\) where \(l\) meets the plane \(\pi\) whose equation is \[\mathbf{r}.\begin{pmatrix}1\\ 2\\ 2\end{pmatrix} = 11.\]
