If u and v are vectors in an inner product space V, then u, v, and u v can be regarded

Chapter 6, Problem 10

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If u and v are vectors in an inner product space V, then u, v, and u v can be regarded as sides of a triangle in V (see the accompanying figure). Prove that the law of cosines holds for any such triangle; that is, u v 2 = u 2 + v 2 2 u v cos where is the angle between u and v.

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