The plane \(\Pi_{1}\) has equation \(\mathbf{r}=\left(\begin{array}{r}2 \\ 3 \\ -1\end{array}\right)+s\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)+t\left(\begin{array}{r}1 \\ -1 \\ -2\end{array}\right)\). Find a cartesian equation of \(\Pi_{1}\).

The plane \(\Pi_{2}\) has equation \(2 x-y+z=10\). Find the acute angle between \(\Pi_{1}\) and \(\Pi_{2}\).

Find an equation of the line of intersection of \(\Pi_{1}\) and \(\Pi_{2}\), giving your answer in the form \(\mathbf{r}=\mathbf{a}+\lambda \mathbf{b}\).