University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.4 - The Cross Product - Exercises - Page 624: 48

Answer

$5$

Work Step by Step

$\overrightarrow{AB} = \langle 1-0, 2-0,0-0 \rangle= \langle 1,2, 0 \rangle$ $\overrightarrow{AC} = \langle 0, -3, 2 \rangle$ $\overrightarrow{AD} = \langle 3, -4, 5 \rangle$ The volume of the parallelepiped is the absolute value of the triple scalar product, $( \overrightarrow{AB}\times \overrightarrow{AC})\cdot \overrightarrow{AD}=\left|\begin{array}{lll} 1 & 2 & 0\\ 0 & -3 & 2\\ 3 & -4 & 5 \end{array}\right|$ $=1(-15+8)-2(0-6)+0$ $=-7+12=5$ $V=|5|=5$
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