University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 15 - Section 15.3 - Path Independence, Conservative Fields, and Potential Functions - Exercises - Page 849: 5

Answer

Not Conservative

Work Step by Step

As we are given that $F=(z+y) i+zj+(y+x) k$ Definition of curl F is: $\text{curl} F =(\dfrac{\partial R}{\partial y}-\dfrac{\partial Q}{\partial z})i +(\dfrac{\partial P}{\partial z}-\dfrac{\partial R}{\partial x}) k+(\dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y})k $ A vector field is conservative iff the $\text{curl} F =0$ Now, curl F$=(1-1) i+(1-1)j +(0-1) k=-k \ne 0$ Hence, the vector field is Not Conservative
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