   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

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 