(a) Show, using vector methods, that the distances from the centroid of a tetrahedron to the centres of opposite pairs of edges are equal. If the three distances are and if are the distances from the centroid to the vertices, show that
[The centroid of points in with position vectors is the point with position vector
(b) Show that
with , is the equation of a right circular double cone whose vertex has position vector a, axis of symmetry and opening angle .
Two such double cones, with vertices and , have parallel axes and the same opening angle. Show that if , then the intersection of the cones lies in a plane with unit normal