(a) Use suffix notation to prove that
(b) Show that the equation of the plane through three non-colinear points with position vectors and is
where is the position vector of a point in this plane.
Find a unit vector normal to the plane in the case and .
(c) Let be the position vector of a point in a given plane. The plane is a distance from the origin and has unit normal vector , where . Write down the equation of this plane.
This plane intersects the sphere with centre at and radius in a circle with centre at and radius . Show that
Find in terms of and . Hence find in terms of and .