Question

Suppose 〈 , 〉 is an inner product on a vector space V . Show that...

Suppose 〈 , 〉 is an inner product on a vector space V . Show that no vectors u and v exist such that

∥u∥ = 1, ∥v∥ = 2, and 〈u, v〉 = −3.

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Answer #1

We know that

Substituting we get

Which contradicts property of inner product that

Thus, it is impossible for there to exist vectors such that

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