assign2_soln

assign2_soln - Math 136 Assignment 2 Solutions 1 Determine...

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Unformatted text preview: Math 136 Assignment 2 Solutions 1. Determine a) proj (2 , 1 , 1) (3 , 2 , 1) and perp (2 , 1 , 1) (3 , 2 , 1). Solution: proj (2 , 1 , 1) (3 , 2 , 1) = (3 , 2 , 1) (2 , 1 , 1) k (2 , 1 , 1) k 2 (2 , 1 , 1) = 9 6 (2 , 1 , 1) = (3 , 3 / 2 , 3 / 2) perp (2 , 1 , 1) (3 , 2 , 1) = (3 , 2 , 1)- proj (2 , 1 , 1) (3 , 2 , 1) = (3 , 2 , 1)- (3 , 3 / 2 , 3 / 2) = (0 , 1 / 2 ,- 1 / 2) b) proj (- 1 , 1 , , 2) (2 ,- 2 , 1 , 1) and perp (- 1 , 1 , , 2) (2 ,- 2 , 1 , 1). Solution: proj (- 1 , 1 , , 2) (2 ,- 2 , 1 , 1) = (2 ,- 2 , 1 , 1) (- 1 , 1 , , 2) k (- 1 , 1 , , 2) k 2 (- 1 , 1 , , 2) =- 2 6 (- 1 , 1 , , 2) = (1 / 3 ,- 1 / 3 , ,- 2 / 3) perp (- 1 , 1 , , 2) (2 ,- 2 , 1 , 1) = (2 ,- 2 , 1 , 1)- proj (- 1 , 1 , , 2) (2 ,- 2 , 1 , 1) = (2 ,- 2 , 1 , 1)- (1 / 3 ,- 1 / 3 , ,- 2 / 3) = (5 / 3 ,- 5 / 3 , 1 , 5 / 3) 2. Use a projection to find the distance from the point to the plane. a) The point P (2 ,- 3 ,- 1) and the plane 2 x 1- 3 x 2- 5 x 3 = 7....
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This note was uploaded on 05/04/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

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assign2_soln - Math 136 Assignment 2 Solutions 1 Determine...

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