assign3_soln

assign3_soln - Math 136 Assignment 3 Solutions 1. Let ~u =...

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Unformatted text preview: Math 136 Assignment 3 Solutions 1. Let ~u = 2 1 3 and ~v = 1- 1 1 . Calculate proj ~v ~u and perp ~v ~u . Solution: We have proj ~v ~u = ~u ~v k ~v k 2 ~v = 4 3 1- 1 1 perp ~v ~u = ~u- proj ~v ~u = 2 1 3 - 4 3 1- 1 1 = 2 / 3 7 / 3 5 / 3 2. Let ~u = 1 2- 3 and ~v = 1 1 . Calculate proj ~v ~u and perp ~v ~u . Solution: We have proj ~v ~u = ~u ~v k ~v k 2 ~v =- 2 2 1 1 = - 1- 1 , perp ~v ~u = ~u- proj ~v ~u = 1 2- 3 - - 1- 1 = 2 2- 2 3. Find the projection of ~v = 1 1 2 onto the plane S = span 1- 2 1 , - 2 1- 2 . Solution: A normal vector of the plane is ~n = 1- 2 1 - 2 1- 2 = 3- 3 ....
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assign3_soln - Math 136 Assignment 3 Solutions 1. Let ~u =...

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