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F_-_Dot___Cross_Products

# F_-_Dot___Cross_Products - Force Vectors Force Dot Product...

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Force Vectors Force Vectors Dot Product Dot Product

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LEARNING OBJECTIVES LEARNING OBJECTIVES Be able to determine an angle between Be able to determine an angle between two vectors. two vectors. Be able to determine the projection of a Be able to determine the projection of a vector along a specified line. vector along a specified line.
PRE-REQUISITE KNOWLEDGE PRE-REQUISITE KNOWLEDGE Units of measurements. Units of measurements. Trigonometry concepts. Trigonometry concepts. Vector concepts. Vector concepts.

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DOT PRODUCT [ ] DOT PRODUCT [ ] θ cos B A AB = Definition of Dot Product of Two Vectors A and B Given the definition 1 k k 0 j k 0 i k 0 k j 1 j j 0 i j 0 k i 0 j i 1 i i = = = = = = = = = j Y Z K i X A B θ
DOT PRODUCT DOT PRODUCT θ cos B A AB = ( 29 ( 29 z z y y x x z y x z y x B A B A B A B B B A A A + + = + + + + = k j i k j i B A Note: Dot product turns two vectors into a scalar A B θ

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DOT PRODUCT-EXAMPLE DOT PRODUCT-EXAMPLE ( 29 ( 29 ° = - = - = - = + + - + + - = = - 07 . 92 0362 . 0 cos ; 0362 . 0 cos 3 cos 6 12 1 5 2 3 3 cos B A Given 1 2 2 2 2 2 2 θ θ θ θ AB Perform dot product between vectors A (3 i + 2 j – 5 k) and B (1 i + 12 j + 6 k) and determine the angle θ between them. ( 29 ( 29 ( 29 3 ) 6 )( 5 ( ) 12 )( 2 ( ) 1 )( 3 ( B A B A k j i k j i B A - = - + + = + + = + + + + = z z y y x x z y x z y x B A B A B A B B B A A A
DOT PRODUCT-LAWS OF OPERATION

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F_-_Dot___Cross_Products - Force Vectors Force Dot Product...

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