Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.5 Curl and Divergence - 16.5 Exercises - Page 1149: 3


a) $ze^xi+(xye^z-yze^x)j-xe^zk$ b) $y(e^z+e^x)$

Work Step by Step

a) When $F=ai+bj+ck$, then we have $curl F=[c_y-b_z]i+[a_z-c_z]j+[b_x-a_y]k$ $curl F=[ze^x-0]i+[xye^z-yze^x]j+[0-xe^z]k=ze^xi+(xye^z-yze^x)j-xe^zk$ b) $div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}=\dfrac{\partial (xye^z)}{\partial x}+\dfrac{\partial (0)}{\partial y}+\dfrac{\partial (yze^x)}{\partial z}=y(e^z+e^x)$
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