   Chapter 16.5, Problem 6E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.6. F(x, y, z) = ln(2y + 3z) i + ln(x + 3z) j + ln(x + 2y) k

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=ln(2y+3z)i+ln(x+3z)j+ln(x+2y)k .

Formula used:

Consider the standard equation of an curl F for F=Pi+Qj+Rk

curlF=|ijkxyzPQR| (1)

Substitute ln(2y+3z) for P , ln(x+3z) for Q and ln(x+2y) for R in equation (1),

curlF=|ijkxyzln(2y+3z)ln(x+3z)ln(x+2y)|={[y(ln(x+2y))z(ln(x+3z))]i[x(ln(x+2y))z(ln(2y+3z))]j+[x(ln(x+3

(b)

To determine

To find: The divergence of the vector field.

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

Define the terms population and sample, and explain the role of each in a research study.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 39-54, simplify the expression. (Assume that x, y, r, s, and t are positive.) 43. x3/4x1/4

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

8. List the operation order for solving equations. (5-2)

Contemporary Mathematics for Business & Consumers

Determine the infinite limit. limx5+x+1x5

Single Variable Calculus: Early Transcendentals

For , f′(x) =

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: converges.

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