Calculus 8th Edition

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

Chapter 16 - Vector Calculus - Review - True-False Quiz - Page 1188: 12



Work Step by Step

Given: curl $\mathbf{F}=xi+yj+zk$ Every vector function $\mathbf{F}$ satisfies the property div (curl $\mathbf{F})= 0$ div curl $\mathbf{F}=div (xi+yj+zk) $ div curl $\mathbf{F}=\frac{∂ (x)}{∂x}+\frac{∂ (y)}{∂y}+\frac{∂ (z)}{∂z} $ div curl $\mathbf{F}=1+1+1 = 3 $ Hence, div (curl $\mathbf{F})\ne 0$ $\mathbf{F}$ cannot exist because div curl $\mathbf{F}$ = 3.
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