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: 4

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

See Property 5 of the cross product (page 714) ${\bf w}={\bf u}\times{\bf 0}={\bf 0}$ (zero vector has length 0 and no direction) ${\bf v}\times{\bf u}=-{\bf w}=(-{\bf 0})={\bf 0}$ ${\bf u}\times{\bf v}$ has length $0$ and no direction ${\bf v}\times{\bf u}$ has length $0$ and no direction
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