   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

Solve the equations in Exercises 112 for x (mentally, if possible). 2x+4=1

Finite Mathematics and Applied Calculus (MindTap Course List)

A sample with a mean of M = 8 has X = 56. How many scores are in the sample?

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

(3, 6)

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

In problems 45-62, perform the indicated operations and simplify. 48.

Mathematical Applications for the Management, Life, and Social Sciences

Given that for all x, a power series for is:

Study Guide for Stewart's Multivariable Calculus, 8th 