Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.4 - The Cross Product - Exercises 12.4 - Page 718: 13

Answer

${\bf( i+j)}\times{\bf (i-j)}=-2{\bf k}$
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Work Step by Step

${\bf u}\times{\bf v}=\left|\begin{array}{lll} {\bf i} & {\bf j} & {\bf k}\\ u_{1} & u_{2} & u_{3}\\ v_{1} & v_{2} & v_{3} \end{array}\right|$ --- ${\bf( i+j)}\times{\bf (i-j)}=\left|\begin{array}{lll} {\bf i} & {\bf j} & {\bf k}\\ 1 & 1 & 0\\ 1 & -1 & 0 \end{array}\right|=(0)-(0)+(-1-1){\bf k}$ $=-2{\bf k}$
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