   Chapter 16, Problem 7RQ

Chapter
Section
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.If F and G are vector fields and div F = div G, then F = G.

To determine

Whether the statement “If F and G are vector fields and divF=divG , then F=G ” is true or false.

Explanation

Formula used:

Write the expression for divergence.

divF=Px+Qy+Rz (1)

Consider the two different three-dimensional vector fields as follows.

F=x,0,0G=0,0,z

Substitute x for P, 0 for Q and 0 for R in equation (1),

divF=(x)x+(0)y+(0)z=1+0+0=1

Modify equation (1) as follows

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Differentiate the function. f(x) = e5

Single Variable Calculus: Early Transcendentals, Volume I

CHECK POINT Which of the following are not real numbers? (a) (b) (c) (d) (e) (f)

Mathematical Applications for the Management, Life, and Social Sciences

The average value of f(x) = 3x2 + 1 on the interval [2, 4] is: a) 29 b) 66 c) 58 d) 36

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 