   Chapter 16.5, Problem 4E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.4. F (x, y, z) = sin yz i + sin zx j + sin xy k

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=sinyzi+sinzxj+sinxyk .

Formula used:

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

curlF=|ijkxyzPQR| (1)

Substitute sinyz for P , sinzx for Q and sinxy for R in equation (1),

curlF=|ijkxyzsinyzsinzxsinxy|={[y(sinxy)z(sinzx)]i[z(sinyz)x(sinxy)]j+[x(sinzx)y(sinyz)]k}={[(x)

(b)

To determine

To find: The divergence of the vector field.

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