Question: If V is an inner product space, prove that the distance function of Definition 5, 3 satisfies the following properties for all vectors u, v,

If V is an inner product space, prove that the distance function of Definition 5, 3 satisfies the following properties for all vectors u, v, and w in V:
(a) d(u. v) ≥ 0
(b) d(u, v) = 0 if and only if u = v
(c) d(u, v) = d(v, u)
(d) d(u, v) ≤ d(u, w) + d(w, v)

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