   Chapter 16.9, Problem 25E

Chapter
Section
Textbook Problem

Prove each identity, assuming that S and E satisfy the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second-order partial derivatives.25. ∬ S a   ⋅ n     d S   =   0 , where a is a constant vector

To determine

To prove: The expression SandS=0 if vector a is a constant vector.

Explanation

Given data:

The vector a is a constant vector.

Formula used:

Write the expression for SandS .

Here,

a is a constant vector,

n is a normal vector to the surface, and

E is the solid region.

Write the expression to find divergence of vector field F(x,y,z)=Pi+Qj+Rk .

divF=xP+yQ+zR (2)

Consider the vector a is as follows.

a=k1i+k2j+k3k

Here,

k1,k2 , and k3 are constants

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