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Use the vector form of the Law of Cosines to show that |u + v|^2 ≤ (|u| + |v|)^2 holds for

any vectors u and v. What does this prove?

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Actually, it's even better than that:

|u + v|^2 ≤ |u|^2 + |v|^2 ≤ (|u|+|v|)^2

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