   Chapter 16, Problem 18RE

Chapter
Section
Textbook Problem

Find curl F and div F if F(x, y, z) = e-x sin y i + e-y sin z j + e-z sin x k

To determine

To Find: Thecurl F if F(x,y,z)=exsinyi+eysinzj+ezsinxk and thediv F if F(x,y,z)=exsinyi+eysinzj+ezsinxk .

Explanation

Given data:

F(x,y,z)=exsinyi+eysinzj+ezsinxk

Formula used:

Write the expression for curlF .

curlF=|ijkxyzPQR| (1)

Write the expression for divF .

divF=Px+Qy+Rz (2)

Write the required differentiation formula.

ddxex=ex

Consider the expression as follows.

F(x,y,z)=exsinyi+eysinzj+ezsinxk (3)

Write the expression for F(x,y,z) .

F(x,y,z)=Pi+Qj+Rk (4)

Compare equation (4) and (2).

P=exsinyQ=eysinzR=ezsinx

Substitute exsiny for P , eysinz for Q and ezsinx for R in equation (1),

curlF=|ijkxyzexsinyeysinzezsinx|={i[(ezsinx)y(eysinz)z]j[(ezsinx

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