2. Problems on Gradient and Divergence Operators Suppose that r is the position vector; that is, r = re, + ye, + ze;, and that r is its magnitude, i.e., r² = x² + y? + 22. Prove the following identities: V.r = 3, V xr = 0, v () --; r p3

2. Problems on Gradient and Divergence Operators Suppose that r is the position vector; that is, r = re, + ye, + ze;, and that r is its magnitude, i.e., r² = x² + y? + 22. Prove the following identities: V.r = 3, V xr = 0, v () --; r p3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

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2. Problems on Gradient and Divergence Operators
Suppose that r is the position vector; that is, r = re, + ye, + ze;, and that r is its
magnitude, i.e., r² = x² + y? + 22. Prove the following identities:
V.r = 3,
V xr = 0,
v () --;
r
p3

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