Explanation Given: The vectors are, 〈 u , v 〉 = 2 u 1 v 1 + u 2 v 2 + u 3 v 3 + ⋯ u n v n .. ( 1 ) u = ( 2 , 3 ) and v = ( 4 , − 1 ) And, u = ( − 2 , − 1 , 2 , 4 ) and v = ( − 3 , 5 , 1 , 1 ) Approach: The angle between two non zero vectors u and v is given by, cos θ = 〈 u , v 〉 ‖ u ‖ ‖ v ‖ … ( 2 ) The magnitude of the vector u = ( a 1 , a 2 ) is given by, ‖ u ‖ = a 1 2 + a 2 2 … ( 3 ) Calculation: For the vectors u = ( 2 , 3 ) and v = ( 4 , − 1 ) , Substitute ( 2 , 3 ) for u and ( 4 , − 1 ) for v in equation ( 1 ) 〈 u , v 〉 = 2 ( 2 ) ( 4 ) + 3 ( − 1 ) = 13 Substitute ( 2 , 3 ) for u in equation ( 3 ) ‖ u ‖ = 2 ( 2 ) 2 + ( 3 ) 2 = 17 Substitute ( 4 , − 1 ) for v in equation ( 3 ) . ‖ v ‖ = 2 ( 4 ) 2 + ( − 1 ) 2 = 33 Substitute 13 for 〈 u , v 〉 , 17 for ‖ u ‖ and 33 for ‖ v ‖ in equation ( 2 ) . cos θ = 13 17 ( 33 ) θ = cos − 1 ( 13 561 ) ≈ 0

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Chapter 5 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - Prob. 6TFR Ch. 5.1 - Prob. 7TFR Ch. 5.1 - Use the standard inner product in 5 to determine...Ch. 5.1 - Prob. 2P Ch. 5.1 - If f(x)=sinx and g(x)=x on [0,], use the function...Ch. 5.1 - If f(x)=sinx and g(x)=2cosx+4 on [0,/2], use the...

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The angle between the vectors u and v .

Solution Summary: The author explains how to determine the angle between two non-zero vectors, namely, langle u,vrangle =2u_1v

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