(a) The plane \(\Pi_1\) has equation \(\mathbf r=-3\mathbf i-\mathbf j-\mathbf k+\lambda(\mathbf j+2\mathbf k)+\mu(\mathbf i+3\mathbf j+\mathbf k)\). Find an equation for \(\Pi_1\) in the form \(ax+by+cz=d\).

(b) Find the perpendicular distance from the point with position vector \(-\mathbf i-2\mathbf k\) to \(\Pi_1\).

(c) The plane \(\Pi_2\) has equation \(3x+2y-z=14\). Find a vector equation of the line of intersection of \(\Pi_1\) and \(\Pi_2\).