The plane \(\Pi_1\) has equation

\(\mathbf r=\begin{pmatrix}5\\1\\0\end{pmatrix}+s\begin{pmatrix}-4\\1\\3\end{pmatrix}+t\begin{pmatrix}0\\1\\2\end{pmatrix}.\)

(i) Find a cartesian equation of \(\Pi_1\).

The plane \(\Pi_2\) has equation \(3x+y-z=3\).

(ii) Find the acute angle between \(\Pi_1\) and \(\Pi_2\), giving your answer in degrees.

(iii) Find an equation of the line of intersection of \(\Pi_1\) and \(\Pi_2\), giving your answer in the form \(\mathbf r=\mathbf a+\lambda\mathbf b\).