Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.4 The Cross Product - Exercises - Page 677: 41


$\sqrt {35}$

Work Step by Step

The area of the parallelogram is calculated as: $||\textbf{u}\times\textbf{v}||$ We take the cross product: $\textbf{u}\times\textbf{v}=\begin{vmatrix}\textbf{i}&\textbf{j}&\textbf{k}\\1&0&3\\2&1&1\end{vmatrix}$ $=\textbf{i}(0\times1-3\times1)-\textbf{j}(1\times1-3\times2)+\textbf{k}(1\times1-0\times2)$ $=-3\textbf{i}+5\textbf{j}+\textbf{k}$ $||\textbf{u}\times\textbf{v}||=\sqrt {(-3)^{2}+5^{2}+1^{2}}=\sqrt {35}$
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