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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: 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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This note was uploaded on 11/25/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.
 Spring '08
 All
 Math, Linear Algebra, Algebra

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