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Unformatted text preview: Lecture 2: Dot Products and Cross Products May 6, 2009 Lecture 2: Dot Products and Cross Products Objectives Dot product concepts 1 Compute dot products 2 Compute angles between vectors 3 Compute projections of vectors Cross product concepts 1 Compute cross products 2 Learn the direction of cross products 3 Compute triple scalar products Lecture 2: Dot Products and Cross Products Dot products a · b = a 1 b 1 + a 2 b 2 + a 3 b 3 Lecture 2: Dot Products and Cross Products Dot products a · b = a 1 b 1 + a 2 b 2 + a 3 b 3 a · b is a scalar. Lecture 2: Dot Products and Cross Products Dot products a · b = a 1 b 1 + a 2 b 2 + a 3 b 3 a · b is a scalar. Properties of the dot product 1 a · a =  a  2 2 a · ( b + c ) = a · b + a · c 3 a · b = b · a 4 a · = 0 5 ( c a ) · b = c ( a · b ) Lecture 2: Dot Products and Cross Products Dot product is related to angle between the vectors Lecture 2: Dot Products and Cross Products Dot product is related to angle between the vectors a · b =  a  b  cos θ Lecture 2: Dot Products and Cross Products Dot product is related to angle between the vectors a · b =  a  b  cos θ cos θ = a · b  a  b  Lecture 2: Dot Products and Cross Products Dot product is related to angle between the vectors...
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 Spring '03
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 Multivariable Calculus, Angles, Vectors, Dot Product, Dot Products

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