Exercise 6.A.13

Answers

Proof. From the Law of Cosines, we have

\begin{aligned} | | u - v | |^{2} & = | | u | |^{2} + | | v | |^{2} - 2 | | u | | | | v | | \cos 𝜃 \\ | | u | |^{2} - 2 ⟨ u, v ⟩ + | | v | |^{2} & = | | u | |^{2} + | | v | |^{2} - 2 | | u | | | | v | | \cos 𝜃 \\ - 2 ⟨ u, v ⟩ & = - 2 | | u | | | | v | | \cos 𝜃 \\ \cos 𝜃 & = \frac{⟨ u, v ⟩}{| | u | | | | v | |} \end{aligned}

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2017-10-06 00:00