If r is the position vector of the point (x, y, z) and A is a constant vector, show that:
(a) (r – A) · A = 0 is the equation of a constant plane
(b) (r – A) · r = 0 is the equation of a sphere
(c) Also show that the result of part (a) is of the form Ax + By + Cz + D = 0 where D = – (A2 + B2 + C2), and that of part (b) Is of the form x2 + y2 + z2 = r2.
(a) (r – A) · A = 0 is the equation of a constant plane
(b) (r – A) · r = 0 is the equation of a sphere
(c) Also show that the result of part (a) is of the form Ax + By + Cz + D = 0 where D = – (A2 + B2 + C2), and that of part (b) Is of the form x2 + y2 + z2 = r2.
