   Chapter 16.5, Problem 3E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.3. F(x, y, z) = xyez i + yzex k

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=xyezi+yzexk .

Formula used:

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

curlF=|ijkxyzPQR| (1)

Substitute xyez for P , 0 for Q and yzex for R in equation (1),

curlF=|ijkxyzxyez0yzex|={[y(yzex)z(0)]i[z(xyez)x(yzex)]j+[x(0)y(xyez)]k

(b)

To determine

To find: The divergence of the vector field.

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