/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 10 Give an example of a conservativ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q. 10 (page 1150)

Give an example of a conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$.

Short Answer

Expert verified

$$F(x, y, z)= \langle x^{2}, y^{2}, z^{2} \rangle$$ is an example of a conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$

Step by step solution

01

Step 1. Given Information

A conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$

02

Step 2. Explanation

Let us take an example, $$x^{2}+y^{2}+z^{2}=16$$

Here, $$F(x, y, z)= \langle x^{2}, y^{2}, z^{2} \rangle$$

Thus, $$F(x, y, z)= \langle x^{2}, y^{2}, z^{2} \rangle$$ is an example of a conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the flux of the given vector field through a permeable membrane described by surface S.

F(x,y,z)=鈭�zi+yj+xk, where S is the surface with the equation y=coszfor 1鈮�x鈮�5and0鈮�z鈮�蟺2.

Let a, b, and c be nonzero constants. Find a general formula for the area of the portion of the plane with equation ax+by+cz=kthat lies above a rectangle [伪,尾]脳[纬,未] in thexy-plane.

Find the work done by the vector field

F(x,y)=cosx2+4xy2i+2y-4x2yj

in moving an object around the unit circle, starting and ending at (1,0).

What are the outputs of a vector field in the Cartesian plane?

Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to x=蟺2 if the force acting on the object at a given value of x is role="math" localid="1650297715748" F(x)=xsinx.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.