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Home  Vectors Product of Vectors Inner Product Theorem 1: Angle Between Vectors |
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Theorem 1: Angle Between Vectors
THEOREM 1 If θ is the angle between two nonzero vectors A and B, then A · B = |A| |B| cos θ. PROOF We give the proof in two dimensions. By the Law of Cosines,
Multiplying through by |A||B|, we have A · B = |A| |B| cos θ.
The angle between two vectors can be easily computed using the inner product. COROLLARY If A and B are nonzero vectors, the angle θ between them has cosine
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Last Update: 2006-11-06