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: 11

Answer

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

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