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assign2_soln

# assign2_soln - Math 136 Assignment 2 Solutions 1 2 3 1 v =...

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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: ˆ u = u u = 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 θ between v and w satisfies cos θ = v · w v w . So, cos θ = 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 . 3. a) Let u = - 1 1 2 and v = 2 3 1 . Calculate proj v u and perp v u . Solution: proj v u = u · v v 2 v = 3 14 2 3 1 = 1 14 6 9 3 perp v u = u - proj v u = - 1 1 2

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assign2_soln - Math 136 Assignment 2 Solutions 1 2 3 1 v =...

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