Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 11 - Vectors and Vector-Valued Functions - 11.4 Cross Products - 11.4 Exercises: 2

Answer

$\theta = arcsin(\frac{|\textbf{u} \times \textbf{v}|}{|\textbf{u}||\textbf{v}|})$

Work Step by Step

Theorem 11.3 : $|\textbf{u} \times \textbf{v}| = |\textbf{u}||\textbf{v}|sin(\theta)$ Solve for $sin(\theta)$ : $sin(\theta) = \frac{|\textbf{u} \times \textbf{v}|}{|\textbf{u}||\textbf{v}|}$ Solve for $\theta$ : $\theta = arcsin(\frac{|\textbf{u} \times \textbf{v}|}{|\textbf{u}||\textbf{v}|})$
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