Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 12 - Vectors and the Geometry of Space - 12.4 Exercises - Page 838: 12

Answer

$(i+j ) \times (i-j)=-2k$

Work Step by Step

Cross product of a vector with itself is zero. We are given $(i+j ) \times (i-j)$ $(i+j ) \times (i-j)=i \times (i-j)+j \times (i-j)$ $=i \times i-i \times j+j\times i-j \times j$ $=0-k+(-k)+0$ $=-2k$ Hence, $(i+j ) \times (i-j)=-2k$
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