Chapter 16, Problem 12RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Show that **F** is a conservative vector field. Then find a function *f* such that **F** = ∇*f*.

**12. F**(*x*,*y*,*z*)* =* sin y **i** + *x* cos *y* **j** − sin *z* **k**

To determine

**To show: F** is a conservative vector field and function

Explanation

**Given data:**

**Formula used:**

Consider the standard equation of an curl **F** for

Find the value of

Substitute
*R* in equation (2),

Simplify expression as follows.

Since
**F** is a conservative vector and the domain of **F** is

Thus, **F** is a conservative vector field is shown.

Consider

Write the relation between the potential function *f* and vector field

Substitute

Compare the equation (3) and equation (1)

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