Chapter 16.5, Problem 31E

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8th Edition

James Stewart

ISBN: 9781285741550

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**/*r*^{3}

(d) ∇ ln *r* = **r**/*r*^{2}

**(a)**

To determine

**To verify:** The vector field of the form

Explanation

**Given data:**

Find

**(b)**

To determine

**To verify:** The vector field of the form

**(c)**

To determine

**To verify:** The vector field of the form

**(d)**

To determine

**To verify:** The vector field of the form

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