   Chapter 16, Problem 10RQ

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.10. If F and G are vector fields, then curI(F · G) = curl F · curl G

To determine

Whether the statement “If F and G are vector fields, then curl(FG)=curlFcurlG ” is true or false.

Explanation

Consider the statement as follows.

curl(FG)=curlFcurlG (1)

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

curlF=|ijkxyzPQR| (2)

Consider the two vector field as follows.

F=xi+yj+zkG=yi+xj+zk

Find the value of curlF .

Substitute x for P , y for Q and z for R in equation (2),

curlF=|ijkxyzxyz|={[y(z)z(y)]i[x(z)z(x)]j+[x(y)y(x)]k}={ij+k}=0

Find the value of curlG .

Modify equation (2) 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

In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 107-120, factor each expression completely. 112. x2 2x 15

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

Factor the following.

Mathematical Applications for the Management, Life, and Social Sciences

Find each product. (4x2y13)(6x+3y)

Elementary Technical Mathematics

If y = f (g(x)) then y′ = f′(g′(x)).

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

Define induction and deduction and explain the role of each in the scientific method.

Research Methods for the Behavioral Sciences (MindTap Course List) 