A plane ∏ passes through the three non-collinear points A, B and C having position vectors a, b and c respectively. Show that the parametric vector equation of the plane ∏ is r = a + λ(b –a) + μ(c – a) The plane ∏ passes through the points (–3, 0, 1), (5, 8, –7) and (2, 1, –2) and the plane Θ passes through the points (3, –1, 1), (1, –2, 1) and (2, –1, 2). Find the parametric vector equation of ∏ and the normal vector equation of Θ , and hence show that their line of intersection is r = (1, –4, –3) + t(5, 1, –3) where t is a scalar variable.