6_Dot_(notes)

# 6_Dot_(notes) - Vector Review Dot Product The dot product...

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Vector Review

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Dot Product The dot product of two vectors a and b is defined a ! b = a b cos " where ! is the angle between a b . 0 ! " ! 180 ! . Sometimes the dot product is called a scalar product. Note: a ! b is a scalar . For what angles is a ! b a maximum? For what angles is a ! b a minimum? a ! b = 0

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Calculating a ! b using components: a ! b = a 1 i + a 2 j ( ) b 1 i + b 2 j ( )
In general a ! b = a 1 b 1 + a 2 b 2 + a 3 b 3 + ... + a n b n ex. a = 0, 0, 3 b = 2 , 0, 2 ! = " 4 ex. Find the angle between a = 1, 2, 3 b = ! 6, 0, 5

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The vector projection of b onto a , proj a b . ex. Find the vector projection of b = ! 6, 0, 5 onto a = 1, 2, 3 .
Work = F ! D = F D cos " . ex. Let a force F = < 3, 4, -1> move an object from P( -1, -2, -3)

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## This note was uploaded on 03/29/2008 for the course MATH 1224 taught by Professor Dontremember during the Spring '08 term at Virginia Tech.

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6_Dot_(notes) - Vector Review Dot Product The dot product...

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