   Chapter 16.5, Problem 8E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.8. F(x, y, z) = ⟨arctan(xy), arctan(yz), arctan(zx)⟩

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=arctan(xy),arctan(yz),arctan(zx) .

Formula used:

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

curlF=|ijkxyzPQR| (1)

Substitute arctan(xy) for P , arctan(yz) for Q and arctan(zx) for R in equation (1),

curlF=|ijkxyzarctan(xy)arctan(yz)arctan(zx)|={[y(arctan(zx))z(arctan(yz))]i[x(arctan(zx))z(arctan(xy))]j+[x(arctan(yz))y(arctan(xy))]k}={[(arctan(zx))y(1)z(

(b)

To determine

To find: The divergence of the vector field.

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