Explanation Given: u = 〈 10 , − 1 〉 , v = 〈 − 2 , − 2 〉 . Formula used: | u | = a 2 + b 2 … ( 1 ) k u = 〈 k a , k b 〉 … ( 2 ) u ± v = 〈 a , b 〉 ± 〈 c , d 〉 = 〈 a ± c , b ± d 〉 … ( 3 ) Here, k is a constant, u = 〈 a , b 〉 = a i + b j , and v = 〈 c , d 〉 = c i + d j . Calculation: Substitute 〈 10 , − 1 〉 for u in expression ( 1 ) . | u | = ( 10 ) 2 + ( − 1 ) 2 = 100 + 1 = 101 Substitute 〈 − 2 , − 2 〉 for v in expression ( 1 ) . | v | = ( − 2 ) 2 + ( − 2 ) 2 = 4 + 4 = 8 = 2 2 Substitute 〈 10 , − 1 〉 for u in expression ( 2 ) . 2 u = 2 〈 10 , − 1 〉 = 〈 20 , − 2 〉 Substitute 〈 20 , − 2 〉 in expression ( 1 ) . | 2 u | = 20 2 + ( − 2 ) 2 = 400 + 4 = 404 = 2 101 Substitute 〈 − 2 , − 2 〉 for v in expression ( 2 ) . 1 2 v = 1 2 〈 − 2 , − 2 〉 = 〈 − 1 , − 1 〉 Substitute 〈 − 1 , − 1 〉 in expression ( 1 )

4th Edition

ISBN: 2818000007824

Author: Stewart

Publisher: CENGAGE L

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Question

Chapter 9.1, Problem 39E

To determine

To find:

|u|, |v|, |2u|, |12v|, |u+v|, |u−v|, |u|−|v|.

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Chapter 9.1, Problem 38E

Chapter 9.1, Problem 40E

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