assign3_soln

# assign3_soln - Math 136 Assignment 3 Due Wednesday Jan 26th...

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Unformatted text preview: Math 136 Assignment 3 Due: Wednesday, Jan 26th 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. Find the projection of ~v = 1 1 2 onto the plane with vector equation ~x = s 1- 2 1 + t - 2 1- 2 , s,t ∈ R Solution: A normal vector of the plane is ~n = 1- 2 1 × - 2 1- 2 = 3- 3 Thus, the projection of ~v onto the plane is perp ~n ~v = ~v- ~v · ~n k ~n k 2 ~n = 1 1 2 -- 3 18 3- 3 = 3 / 2 1 3 / 2 3. Let ~x ∈ R n and c ∈ R . Prove that k c~x k = | c |k ~x k . Solution: Let ~x = x 1 . . . x n . Then k c~x k 2 = cx 1 ....
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assign3_soln - Math 136 Assignment 3 Due Wednesday Jan 26th...

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