Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises: 13

Answer

i $\bullet$ j = j $\bullet$ k =k $\bullet$ i =0 i $\bullet$ i = j $\bullet$ j =k $\bullet$ k =1

Work Step by Step

a) i $\bullet$ j = <1,0,0> $\bullet$ <0,1,0> is: 0×0 + 0×0 + 0×0 = 0 j $\bullet$ k = <0,1,0> $\bullet$ <0,0,1> is: 0×0 + 0×0 + 0×0 = 0 k $\bullet$ i = <0,0,1> $\bullet$ <1,0,0> is: 0×0 + 0×0 + 0×0 = 0 b) i $\bullet$ i = <1,0,0> $\bullet$ <1,0,0> is: 1×1 + 0×0 + 0×0 = 1 j $\bullet$ j = <0,1,0> $\bullet$ <0,1,0> is: 0×0 + 1×1 + 0×0 = 1 k $\bullet$ k = <0,0,1> $\bullet$ <0,0,1> is: 0×0 + 0×0 + 1×1 = 1
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