lecture03 - B Scalar product (dot product) A A B | A | B |...

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Scalar product (dot product) z z y y x x B A B A B A B A B A cos | || | A B Properties of the dot product A A A A C A B A C B A A B B A 2 2 ) ( Angle between vectors: | || | cos B A B A k A A j A A i A A z y x ˆ ˆ ˆ Projections A B AB B A B A || ||
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cos || A A B cos || B B A A B AB B A B A || || B projected onto A : Component of A perpendicular to B : sin B B A sin A A B A projected onto B : Component of B perpendicular to A : Projections A B A B A B A B
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Example: Which pair of vectors will have the largest value for A·B? A A B C B A B 60° A B 30° A·B = AB cos60° A·B =AB cos90°= 0 A·B = AB cos30° More visual: A · B = B A projected onto B A projected onto B A projected onto B A projected onto B
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This note was uploaded on 10/21/2010 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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lecture03 - B Scalar product (dot product) A A B | A | B |...

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