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: 15


NOT conservative

Work Step by Step

The vector field $F$ is conservative when $curl F=0$ When $F=ai+bj+ck$, then we have $curl F=[c_y-b_z]i+[a_z-c_z]j+[b_x-a_y]k$ $curl F=(6x^2yz^2-6x^2yz^2)i+(6xy^2z-6xy^2z^2)j+(4xyz^3-6xyz^2)k \ne 0$ Thus, the vector field $F$ is NOT conservative because $curl F \ne 0$.
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