Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 16: Integrals and Vector Fields - Practice Exercises - Page 1029: 29



Work Step by Step

A vector field is said to be conservative when $ curl \space F=\nabla \times F=0$ Thus, $$ curl \space F= \nabla \times F=(\dfrac{\partial z}{\partial y}-\dfrac{\partial y}{\partial z}) \space i+(\dfrac{\partial x}{\partial z}-\dfrac{\partial z}{\partial x}) \space j+(\dfrac{\partial y}{\partial x}-\dfrac{\partial x}{\partial y}) \space k $$ From the given equation, we have $ curl F=(0-0)i+(0-0)j+(0-0) k=0$ Thus, the given field $ F $ is conservative.
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