6. Prove Theorem 5.9 (a) and (b). Theorem 5.9. Let S be an orthonormal basis for an n-dimensional inner product space V. If the coordinate vectors of u and v relative to the basis S are given by [u]s = [u₁, U2,..., un] and [v]s = [V₁, V2,..., Un], then + u²₂/12. (a) ||u|| = √√u²+uz+ (b) d(u, v) = √(u₁ − v₁)² + (u₂ − v₂)² +….. + (un - vn)².

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