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 1150: 29


$curl (curl F)=grad(div F) -\nabla^2 F$

Work Step by Step

We will have to show that $curl (curl F)=grad(div F) -\nabla^2 F$ $curl (curl F)=\nabla \times (\nabla \times F)$ $=\nabla (\nabla \cdot F) -F (\nabla \cdot \nabla)$ $=\nabla (div F) -F (\nabla^2)$ Hence, the result has been proved. $curl (curl F)=grad(div F) -\nabla^2 F$
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