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assign3_soln

# assign3_soln - Math 136 Assignment 3 Solutions 2 1 1 and v...

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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 0 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 0 1 = - 1 0 - 1 , perp ~v ~u = ~u - proj ~v ~u = 1 2 - 3 - - 1 0 - 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 0 - 3 . To project ~v onto the plane S , we find the perpendicular of the projection of ~v onto the normal vector. Thus, the projection of ~v onto the plane S is perp ~n ~v = ~v - ~v · ~n k ~n k 2 ~n = 1 1 2 - - 3 18

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assign3_soln - Math 136 Assignment 3 Solutions 2 1 1 and v...

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