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: 38


20 cubic units.

Work Step by Step

The volume of the parallelepiped is given as: $\textbf{u}\cdot(\textbf{v}\times\textbf{w})$ = det $\begin{pmatrix}u\\v\\w\end{pmatrix}$ $=\begin{vmatrix}2&2&1\\1&0&3\\0&-4&0\end{vmatrix}$ $=0-[-4(2\times3-1\times1)]+0$ (As there are two zeros in the third row, evaluation of the determinant by the expansion along the third row is easy.) =20 cubic units.
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