   Chapter 16.5, Problem 22E

Chapter
Section
Textbook Problem

Show that any vector field of the formF(x, y, z) = f(y, z) i + g(x, z) j + h(x, y) kis incompressible.

To determine

To show: The vector field of the form F(x,y,z)=f(y,z)i+g(x,z)j+h(x,y)k is incompressible.

Explanation

Given data:

F(x,y,z)=f(y,z)i+g(x,z)j+h(x,y)k

Formula used:

Consider the standard equation of a divergence of vector field for F=Pi+Qj+Rk

divF=Px+Qy+Rz (1)

Substitute f(y,z) for P , g(x,z) for Q and h(x,y) for R in equation (1),

divF=x[f(y,z)]+y[g(x,z)]+z[h(x,y

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