Find a cartesian equation of the plane \(\Pi\) containing the lines
\(\mathbf{r}=3 \mathbf{i}+\mathbf{k}+s(2 \mathbf{i}+\mathbf{j}-\mathbf{k}) \quad \text { and } \quad \mathbf{r}=3 \mathbf{i}-7 \mathbf{j}+10 \mathbf{k}+t(\mathbf{i}-3 \mathbf{j}+4 \mathbf{k})\)

The line \(l\) passes through the point \(P\) with position vector \(6 \mathbf{i}-2 \mathbf{j}+\mathbf{k}\) and is parallel to the vector \(2 \mathbf{i}+\mathbf{j}-4 \mathbf{k}\). Find
(i) the position vector of the point where \(l\) meets \(\Pi\),

(ii) the perpendicular distance from \(P\) to \(\Pi\),

(iii) the acute angle between \(l\) and \(\Pi\).