N2015 P2 Q2

The line \(L\) has equation \(\mathbf r=\mathbf i-2\mathbf j-4\mathbf k+\lambda(2\mathbf i+3\mathbf j-6\mathbf k)\).

1. Find the acute angle between \(L\) and the \(x\)-axis.[2]

The point \(P\) has position vector \(2\mathbf i+5\mathbf j-6\mathbf k\).

2. Find the points on \(L\) which are a distance of \(\sqrt{33}\) from \(P\). Hence or otherwise find the point on \(L\) which is closest to \(P\).[5]
3. Find a cartesian equation of the plane that includes the line \(L\) and the point \(P\).[3]