5_Dot - to Q(1 2 3 Find the work done Do 1 Let a = 10 11-2...

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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 θ where θ is the angle between a and b . 0 θ 180 o . 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 Calculating a b using components:

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a b = a 1 i + a 2 j (29 b 1 i + b 2 j (29 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 θ = π 4 ex. Find the angle between a = 1 , 2 , 3 b =- 6 , 0 , 5 The vector projection of b onto a , proj a b .

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

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Unformatted text preview: to Q(1, 2, 3). Find the work done. Do: 1. Let a = 10 , 11 , -2 b = , 3 , 4 a. Find a ⋅ b . b. Find the cosine of the angle between a and b . c. Find the vector projection of a onto b . 2. Find the work done by a force of 20 pounds acting in the direction N 30 o W in moving an object 4 feet due west. 3. Are the following vectors orthogonal, parallel or neither? a . u = 2 , 1 , -5 v = 4 , 2 , 1 b . u = 2 , 1 , -5 v = 4 , 2 , -10 c . u = 2 , 1 , -5 v = 4 , 2 , 2...
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