The plane \(\Pi_{1}\) has parametric equation
\(\mathbf{r}=2 \mathbf{i}-3 \mathbf{j}+\mathbf{k}+\lambda(\mathbf{i}-2 \mathbf{j}-\mathbf{k})+\mu(\mathbf{i}+2 \mathbf{j}-2 \mathbf{k}) .\)

Find a cartesian equation of \(\Pi_{1}\).

The plane \(\Pi_{2}\) has cartesian equation \(3 x-2 y-3 z=4\). Find the acute angle between \(\Pi_{1}\) and \(\Pi_{2}\).

Find a vector equation of the line of intersection of \(\Pi_{1}\) and \(\Pi_{2}\).