Chapter 16, Problem 12RQ

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

There is a vector field **F** such that curl **F** = *x*i + *y*j + *z*k

To determine

Whether the statement “there is a vector field **F** such that

Explanation

Consider a three dimensional vector field such as

The curl of vector field **F** can be written as follows.

Substitute *x* for
*y* for
*z* for

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