Let V be an inner product space. (a) Prove that (x. v) = 0 for all v

Question:

Let V be an inner product space.
(a) Prove that (x. v) = 0 for all v € V if and only if x = 0.
(b) Prove that (x. v) = (y. v) for all v e V if and only if x = y.
(c) Let v1,...,vn be a basis for V. Prove that (x, v,) = (y, vj), i = 1,.... n, if and only if x = y.