The plane \(\Pi_{1}\) passes through the points \((1,2,1)\) and \((5,-2,9)\) and is parallel to the vector \(\mathbf{i}+2 \mathbf{j}+3 \mathbf{k}\).
(i) Find the cartesian equation of \(\Pi_{1}\).

The plane \(\Pi_{2}\) contains the lines
\(\mathbf{r}=2 \mathbf{i}-3 \mathbf{j}+\mathbf{k}+\lambda(\mathbf{i}-2 \mathbf{j}-\mathbf{k}) \quad \text { and } \quad \mathbf{r}=2 \mathbf{i}-3 \mathbf{j}+\mathbf{k}+\mu(2 \mathbf{i}+3 \mathbf{j}-\mathbf{k}) .\)
(ii) Find the cartesian equation of \(\Pi_{2}\).

(iii) Find the acute angle between \(\Pi_{1}\) and \(\Pi_{2}\).