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: 1


a) 0 b) $y^2z^2+x^2z^2+x^2y^2$

Work Step by Step

a) When $F=ai+bj+ck$, then we have $curl F=[c_y-b_z]i+[a_z-c_z]j+[b_x-a_y]k$ $curl F=[2x^2yz-2x^2yz]i+[2xy^2z-2xy^2z]j+[2xyz^2-2xyz^2]k=0$ b) $div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}=\dfrac{\partial (xy^2z^2)}{\partial x}+\dfrac{\partial (x^2yz^2)}{\partial y}+\dfrac{\partial (x^2y^2z)}{\partial z}=y^2z^2+x^2z^2+x^2y^2$
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