Lecture_4-Dot_Product-1.ppt

# Lecture_4-Dot_Product-1.ppt - Force Vectors Lecture 4Dot...

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Force Vectors Lecture 4-Dot Product (section 2.9)

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Learning Objectives Be able to determine an angle between two vectors. Be able to determine the projection of a vector along a  specified line.
Pre-requisite Knowledge Units of measurements. Trigonometry concepts. Vector concepts. Unit vectors.

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Dot Product θ cos B A = B A ( 29 ( 29 z z y y x x z y x z y x B A B A B A k B j B i B k A j A i A + + = + + + + = B A Definition of dot product: Note: Dot product turns two vectors into a scalar
( 29 ( 29 ° = - = - = + + - + + = - = - 07 . 92 0362 . 0 cos 0362 . 0 cos cos 6 12 1 5 2 3 3 cos B A 1 2 2 2 2 2 2 θ B A Given: Vectors A and B are (3 i + 2 j – 5 k) and (1 i + 12 j + 6 k) ( 29 ( 29 ( 29 ( 29 ( 29 3 6 5 12 2 1 3 B A - = - + + = + + + + = k B j B i B k A j x Angle between vectors A and B: Dot product between vectors A and B:

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## This note was uploaded on 06/14/2009 for the course CE 221 taught by Professor Buch during the Spring '08 term at Michigan State University.

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Lecture_4-Dot_Product-1.ppt - Force Vectors Lecture 4Dot...

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