Calculus (3rd Edition)

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

Chapter 13 - Vector Geometry - Chapter Review Exercises - Page 702: 25


48 cubic units.

Work Step by Step

The volume of the parallelepiped is given as: $|\textbf{u}\cdot (\textbf{v}\times\textbf{w})|$ We calculate the dot product and cross product as follows: $\textbf{u}\cdot (\textbf{v}\times\textbf{w})$= det $\begin{pmatrix}u\\v\\w\end{pmatrix}$ $=\begin{vmatrix}1&2&6\\1&3&-2\\2&-1&4\end{vmatrix}$ $=1(3\times4-(-1\times-2))-2(1\times4-2\times-2)+6(1\times-1-2\times3)$ $=10-16-42=-48$ Volume= $|\textbf{u}\cdot (\textbf{v}\times\textbf{w})|=48$
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