   Chapter 16.5, Problem 2E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.2. F(x, y, z) = x3yz2 j + y4z3 k

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=x3yz2j+y4z3k .

Formula used:

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

curlF=|ijkxyzPQR| (1)

Substitute 0 for P , x3yz2 for Q and y4z3 for R in equation (1),

curlF=|ijkxyz0x3yz2y4z3|={[y(y4z3)z(x3yz2)]i[z(0)x(y4z3)]j+[x(x3yz2)y(0)]k}={[</

(b)

To determine

To find: The divergence of the vector field.

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