   Chapter 16.5, Problem 7E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.7. F(x, y, z) = ⟨ex sin y, ey sin z, ez sin x⟩

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=exsiny,eysinz,ezsinx .

Formula used:

Consider the standard equation of an curl F for F=P,Q,R .

curlF=|ijkxyzPQR| (1)

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

curlF=|ijkxyzexsinyeysinzezsinx|={[y(ezsinx)z(eysinz)]i[x(ezsinx)z(exsiny)]j+[x(eysinz)y(ex </

(b)

To determine

To find: The divergence of the vector field.

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