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 623: 33


No. See counterexample below.

Work Step by Step

Build a counterexample using parallel vectors. Let ${\bf u}$ =${\bf i, \ \ v}$ =${\bf -i,\ \ w}$ =${\bf 2i}.$ The cross products ${\bf u}\times{\bf v}$ and ${\bf u}\times{\bf w}$ both equal ${\bf 0}$ because the cross product of parallel vectors is the zero vector. So, we have ${\bf u}\times{\bf v}={\bf u}\times{\bf w}, \quad {\bf u}\neq {\bf 0}$, but ${\bf v}\neq {\bf w}$
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