University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.4 - The Cross Product - Exercises - Page 622: 3

Answer

${\bf u}\times{\bf v}$ has length $0$ and no direction ${\bf v}\times{\bf u}$ has length $0$ and no direction

Work Step by Step

${\bf w}={\bf u}\times{\bf v}=\left|\begin{array}{lll} {\bf i} & {\bf j} & {\bf k}\\ 2 & -2 & 4\\ -1 & 1 & -2 \end{array}\right|$ $=(4-4){\bf i}-(-4+4){\bf j}+(22){\bf k}$ $={\bf 0}$ (zero vector has length 0 and no direction) By property 3 (see "Properties of the Cross Product" box on p. 618) ${\bf v}\times{\bf u}=-{\bf w}=(-{\bf 0})={\bf 0}$ ${\bf v}\times{\bf u}$ has length $0$ and no direction
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