Let V be an inner product space. Show the following:
(a) ||0||=0.
(b) (u, 0) = (0, u) = 0 for any u in V.
(c) If (u, v) = 0 for all v in V, then u = 0.
(d) If (u, w) = (v, w) for all w in V, then u = v.
(e) If (w, u) = (w, v) for all w in V, then u = v.