F - Dot &amp; Cross Products Angel

# F - Dot &amp; Cross Products Angel - Force Vectors...

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Unformatted text preview: Force Vectors Force Vectors Dot Product Dot Product 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. 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 j k i k k j 1 j j i j k i j i 1 i i = • = • = • = • = • = • = • = • = • j Y Z K i A B 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 DOT PRODUCT-EXAMPLE DOT PRODUCT-EXAMPLE ( 29 ( 29 ° =-= →-=-= + + -+ +-= = •-07 . 92 0362 . cos ; 0362 . cos 3 cos 6 12 1 5 2 3 3 cos B A Given 1 2 2 2 2 2 2 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....
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F - Dot &amp; Cross Products Angel - Force Vectors...

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