Explanation Approach: If u = 〈 a , b 〉 and v = 〈 c , d 〉 are vectors , then the dot product of u and v is denoted by u ⋅ v , and defined by u ⋅ v = a c + b d . If c is a scalar, then ( c u ) is defined by c 〈 a , b 〉 = 〈 a c , b c 〉 . Calculation: Consider the vectors u = 〈 a 1 , a 2 〉 and v = 〈 b 1 , b 2 〉 . Consider, ( c u ) ⋅ v = c 〈 a 1 , a 2 〉 ⋅ 〈 b 1 , b 2 〉 = 〈 a 1 c , a 2 c 〉 ⋅ 〈 b 1 , b 2 〉 = ( a 1 c ) ( b 1 ) + ( a 2 c ) ( b 2 ) = a 1 b 1 c + a 2 b 2 c … ( 1 ) Consider, c ( v ⋅ u ) = c [ 〈 a 1 , a 2 〉 ⋅ 〈 b 1 , b 2 〉 ] = c [ ( a 1 ) ( b 1 ) + ( a 2 ) ( b 2 ) ] = c [ a 1 b 1 + a 2 b 2 ] = a 1 b 1 c + a 2 b 2 c … ( 2 ) Consider,

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Question

Chapter 9.2, Problem 40E

To determine

To prove:

The property (cu)⋅v=c(v⋅u)=u⋅(cv).

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Chapter 9.2, Problem 39E

Chapter 9.2, Problem 41E

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