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

Find a vector normal to \(\Pi_{1}\) and hence show that the equation of \(\Pi_{1}\) can be written as \(2 x+3 y+6 z=14\).

The line \(l\) has equation
\(\mathbf{r}=3 \mathbf{i}+8 \mathbf{j}+2 \mathbf{k}+t(4 \mathbf{i}+6 \mathbf{j}+5 \mathbf{k})\)

The point on \(l\) where \(t=\lambda\) is denoted by \(P\). Find the set of values of \(\lambda\) for which the perpendicular distance of \(P\) from \(\Pi_{1}\) is not greater than 4 .

The plane \(\Pi_{2}\) contains \(l\) and the point with position vector \(\mathbf{i}+2 \mathbf{j}+\mathbf{k}\). Find the acute angle between \(\Pi_{1}\) and \(\Pi_{2}\).