12.9 Parallel & Perpendicular Vectors in Two Dimensions

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Presentation transcript:

12.9 Parallel & Perpendicular Vectors in Two Dimensions

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) 29 7 0 should be 13 Perpendicular vectors have a dot product of 0 called orthogonal vectors.

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

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.

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:

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)

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