Homework_10_solution - MA 265 HOMEWORK ASSIGNMENT#10 SOLUTIONS#1 Page 297 Exercise 2 In Exercises 1 and 2 find the length of each vector(a 2(b 1 3

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Unformatted text preview: MA 265 HOMEWORK ASSIGNMENT #10 SOLUTIONS #1. Page 297; Exercise 2. In Exercises 1 and 2, find the length of each vector. (a) - 2 (b) - 1- 3- 4 (c) 1- 2 4 Solution: (a) We define the 3-vector v = - 2 = || v || = p 2 + (- 2) 2 + 0 2 = 4 = 2 (b) We define the 3-vector v = - 1- 3- 4 = || v || = p (- 1) 2 + (- 3) 2 + (- 4) 2 = 26 (c) We define the 3-vector v = 1- 2 4 = || v || = p 1 2 + (- 2) 2 + 4 2 = 21 #2. Page 297; Exercise 6. In Exercises 5 and 6, find the distance between u and v . (a) u = - 1- 2- 3 , v = 4 5 6 (b) u = 1- 1 , v = 1 2 . Solution: (a) We have the two 3-vectors u = - 1- 2- 3 and v = 4 5 6 = || v- u || = q (4- (- 1)) 2 + (5- (- 2)) 2 + (6- (- 3)) 2 = p 5 2 + 7 2 + 9 2 = 155 1 2 MA 265 HOMEWORK ASSIGNMENT #10 SOLUTIONS (b) We have the two 3-vectors u = 1- 1 and v = 1 2 = || v- u || = q (1- 0) 2 + (2- 1) 2 + (0- (- 1)) 2 = p 1 2 + 1 2 + 1 2 = 3 #3. Page 297; Exercise 8. In Exercises 7 and 8, determine all values of c so that each given condition is satisfied. || u || = 1 for u = 1 c 2 c- 2 c Solution: The length of the vector is || u || = q ( 1 c ) 2 + ( 2 c ) 2 + (- 2 c ) 2 = q 1 c 2 + 4 c 2 + 4 c 2 = q 9 c 2 = 3 | c | . Since we want || u || = 1, we must have | c | = 3, i.e., c = 3. #4. Page 297; Exercise 10. For each pair of vectors in Exercise 6, find the cosine of the angle between u and v . Solution: (a) We have the two 3-vectors u = - 1- 2- 3 and v = 4 5 6 = cos = u v || u |||| v || = (- 1)(4) + (- 2)(5) + (- 3)(6) p (- 1) 2 + (- 2) 2 + (- 3) 2 4 2 + 5 2 + 6 2 =- 32 14 77 (b) We have the two 3-vectors u = 1- 1 and v = 1 2 = cos = u v || u |||| v || = (0)(1) + (1)(2) + (- 1)(0) p 2 + 1 2 + (- 1) 2 1 2 + 2 2 + 0 2 = 2 2 5 #5. Page 298; Exercise 18. Which of the vectors v 1 = 1- 1- 2 , v 2 = 3- 1 2 , v 3 = 2 4- 1 , v 4 = 1 2 1 4 , v 5 = 1 2- 1 2- 1 , v 6 = - 2 3- 4 3 1 3 ....
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This note was uploaded on 03/11/2010 for the course MA 261A 0026100 taught by Professor ... during the Spring '10 term at Purdue University Calumet.

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Homework_10_solution - MA 265 HOMEWORK ASSIGNMENT#10 SOLUTIONS#1 Page 297 Exercise 2 In Exercises 1 and 2 find the length of each vector(a 2(b 1 3

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