assign2_soln

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

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Unformatted text preview: Math 136 Assignment 2 Solutions 1. Let ~u = - 1 1 3 , ~v = 2- 1- 1 , and ~w = 3 1 2 . a) Find a unit vector in the direction of ~u . Solution: u = ~u k ~u k = 1 1+1+9 - 1 1 3 = 1 11 - 1 1 3 . b) Determine the angle between ~v and ~w . Solution: We know that the angle between ~v and ~w satisfies cos = ~v ~w k ~v kk ~w k . So, cos = 6- 1- 2 6 14 = 3 84 . Hence, the angle between ~v and ~w is arccos 3 84 . c) Show that ~u and ~v are not orthogonal. Solution: We have ~u ~v = (- 1)(2)+1(- 1)+(3)(- 1) =- 6, hence ~u and ~v are not orthogonal. 2. Determine all values of k for which 1 2 1 and k 2 k 4 are orthogonal. Solution: We have 1 2 1 k 2 k 4 = k + 4 k + 4 = 5 k + 4 . Hence, the vectors are orthogonal if 5 k + 4 = 0 or k =- 4 5 ....
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This note was uploaded on 09/19/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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

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