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Published byMagnus Holland Modified over 6 years ago
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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: it’s a number! (not a vector) Ex 1) Two Truths & a Lie Find the dot product. A) B) C) 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.
θ 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!
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Example: Let a = (8, -4) and b = (2, 1) Show that a b = b a
Find the angle between a and b to the nearest tenth of a degree Find a vector that is parallel to a. Find a vector that is perpendicular to a.
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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) (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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Exit Slip 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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