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assign2_soln

# assign2_soln - Math 136 Assignment 2 Solutions 1 Let ~u = 3...

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Unformatted text preview: Math 136 Assignment 2 Solutions 1. Let ~u = 3 2- 2 , and ~v = 1 3- 1 . a) Find a unit vector in the direction of ~u . Solution: ˆ u = ~u k ~u k = 1 √ 9+4+4 3 2- 2 = 1 √ 17 3 2- 2 . b) Determine ~u · ~v . Are ~u and ~v orthogonal? Solution: ~u · ~v = 3(1) + 2(3) + (- 2)(- 1) = 11. Since ~u · ~v 6 = ~ 0, they are not orthogonal. 2. a) Let ~u = 7 1- 1 and ~v = - 1 3- 3 . Calculate proj ~v ~u and perp ~v ~u . Solution: proj ~v ~u = ~u · ~v k ~v k 2 ~v =- 1 19 - 1 3- 3 = 1 / 19- 3 / 19 3 / 19 perp ~v ~u = ~u- proj ~v ~u = 7 1- 1 - 1 / 19- 3 / 19 3 / 19 = 132 / 19 22 / 19- 22 / 19 . b) Let ~u = 2- 1 3- 4 and ~v = 1 1 . Calculate proj ~v ~u and perp ~v ~u . Solution: proj ~v ~u = ~u · ~v k ~v k 2 ~v =- 2 2 1 1 = - 1- 1 perp ~v ~u = ~u- proj ~v ~u...
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assign2_soln - Math 136 Assignment 2 Solutions 1 Let ~u = 3...

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