10.3 , 10.4 notes - Slide 1 The Dot Product of Two Vectors...

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Slide 1 The Dot Product of Two Vectors Section 10.3 Slide 2 Definition of Dot Product The dot product of and is The dot product of and is 2 1 , u u u = 2 1 , v v v = 2 2 1 1 v u v u v u + = 3 2 1 , , u u u u = 3 2 1 , , v v v v = 3 3 2 2 1 1 v u v u v u v u + + = Slide 3 Properties of Dot Product Let u , v , and w be vectors in the plane or in space and let c be a scalar. u v v u = ( 29 w u v u w v u + = + ( 29 v c u v u c v u c = = 0 0 = v 2 v v v =
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Slide 4 Angle Between Two Vectors If θ is the angle between two nonzero vectors u and v , then Note that you can rewrite the formula above to get an alternative form of the dot product. v u v u = θ cos cos v u v u = Slide 5 Orthogonal Vectors The vectors u and v are orthogonal if u v = 0. What is the difference between perpendicular, orthogonal, and normal? Slide 6 Direction Cosines The direction angle for a vector in the plane is measured counterclockwise from the positive x- axis to the vector. In space we measure direction in terms of the
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10.3 , 10.4 notes - Slide 1 The Dot Product of Two Vectors...

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