Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 15 - Vector Analysis - 15.1 Exercises - Page 1050: 62

Answer

11

Work Step by Step

div $\textbf{F}=\nabla\cdot \textbf{F}=\nabla\cdot\langle x^{2}z,-2xz,yz\rangle$ $=\frac{\partial}{\partial x}(x^{2}z)+\frac{\partial}{\partial y}(-2xz)+\frac{\partial}{\partial z}(yz)$ $=2xz+0+y=2xz+y$ Knowing that $(x,y,z)=(2,-1,3)$, We get div $\textbf{F}=2\times2\times3+(-1)=11$
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