   Chapter 16.5, Problem 5E

Chapter
Section
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.5. x, y, z) = i + j + k

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=x1+zi+y1+xj+z1+yk .

Formula used:

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

curlF=|ijkxyzPQR| (1)

Substitute x1+z for P , y1+x for Q and z1+y for R in equation (1),

curlF=|ijkxyzx1+zy1+xz1+y|={[y(z1+y)z(y1+x)]i[x(z1+y)z(x1+z)]j+[x(y1+x)y(x1+z)]k}={

(b)

To determine

To find: The divergence of the vector field.

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