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 719: 33


No. Counterexample given below.

Work Step by Step

Build a counterexample. Let ${\bf u}$ =${\bf i, v}$ =${\bf 2i,w}$ =${\bf 3i}., $ 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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