   Chapter 16.5, Problem 31E

Chapter
Section
Textbook Problem

Let r = x i + y j + z k and r = |r|.31. Verify each identity.(a) ∇r = r/r(b) ∇ × r = 0(c) ∇(1/r) = −r/r3(d) ∇ ln r = r/r2

(a)

To determine

To verify: The vector field of the form r=rr .

Explanation

Given data:

r=xi+yj+zk

Find r .

r=(xi+yj+zk)(|xi+yj+zk|)=(xi+yj+zk)(x2+y2+z2)=x(x2+y2+z2)i+yy(x2+y2+z2)j+zz(x2+y2+z2)k=[12(x2+y2+z2)12

(b)

To determine

To verify: The vector field of the form ×r=0 .

(c)

To determine

To verify: The vector field of the form (1r)=rr3 .

(d)

To determine

To verify: The vector field of the form lnr=rr2 .

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

Solve the following problems and reduce to lowest terms. 13.

Contemporary Mathematics for Business & Consumers

Multiply: (3)(+3)(4)

Elementary Technical Mathematics

For , an upper bound estimate for s − s6 (where s6 is the sixth the series does not converge

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 