This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 3vector v =  2 =  v  = p 2 + ( 2) 2 + 0 2 = 4 = 2 (b) We define the 3vector v =  1 3 4 =  v  = p ( 1) 2 + ( 3) 2 + ( 4) 2 = 26 (c) We define the 3vector 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 3vectors 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 3vectors 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 3vectors 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 3vectors 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 ....
View
Full
Document
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.
 Spring '10
 ...

Click to edit the document details