   Chapter 16.5, Problem 1E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.1. F(x, y, z) = xy2z2 i + x2yz2 j + x2y2z k

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=xy2z2i+x2yz2j+x2y2zk .

Formula used:

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

curlF=|ijkxyzPQR| (1)

Substitute xy2z2 for P , x2yz2 for Q and x2y2z for R in equation (1),

curlF=|ijkxyzxy2z2x2yz2x2y2z|={[y(x2y2z)z(x2yz2)]i[z(xy2z2)x(x2y2z)]j+[x(x2yz2)y(xy2z2)]k}

(b)

To determine

To find: The divergence of the vector field.

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