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12.9 Parallel & Perpendicular Vectors in Two Dimensions

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If we have cv, it is a scalar multiplied times a vector. What about a vector times a vector? Dot Product: its a number! (not a vector) Ex 1) Two Truths & a Lie Find the dot product. A) B) C) 297 0 should be 13 Perpendicular vectors have a dot product of 0 called orthogonal vectors.

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We can utilize the Law of Cosines to find the angle between any two vectors. Ex 2) Find the measure of the angle between vectors

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Parallel vectors have the same slope, they are scalar multiples of each other. watch out! Ex 3) We need to be able to tell if 2 vectors are parallel, perpendicular, or neither using the dot products. Choose two different options (between , , & N) Make up 2 questions of your own. Trade with a partner & solve theirs.

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Ex 4) Determine the value of K for which each pair of vectors is parallel and the value of K for which they are perpendicular. Perpendicular: Parallel:

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An important application of the dot product in physics is work done on a body through distance. Work = Force displacement (vector) Ex 5) Determine the work done by a force of magnitude (newtons) in moving a box 20 m along a floor that makes an angle of 30 with. Give answers in newton-meters (N-m) (joules = newton-meters)

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Properties of the Dot Product Norm Commutative Property Distributive Property Associative Property Scalar

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Homework #1209 Pg 657 #1, 8, 11, 13, 15, 18, 20, 23, 25, 27, 29, 33, 35