Calculate the divergence and the curl of this vector function.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Consider the following vector function: A = (6xy)x+ (3x²)ŷ + (4z)2
a) Calculate the divergence and the curl of this vector function.
b) Calculate the path integral of this vector function from the origin to the point (1,1,1) using two different
paths: 1) going in the direction from (0,0,0) to (1,0,0), then the y direction from (1,0,0) to (1,1,0), then
the 2 direction from (1,1,0) to (1,1,1) and 2) going in a straight line from (0,0,0) to (1,1,1).
c) Are the results of parts a) and b) consistent with each other? Explain why or why not.
Transcribed Image Text:Consider the following vector function: A = (6xy)x+ (3x²)ŷ + (4z)2 a) Calculate the divergence and the curl of this vector function. b) Calculate the path integral of this vector function from the origin to the point (1,1,1) using two different paths: 1) going in the direction from (0,0,0) to (1,0,0), then the y direction from (1,0,0) to (1,1,0), then the 2 direction from (1,1,0) to (1,1,1) and 2) going in a straight line from (0,0,0) to (1,1,1). c) Are the results of parts a) and b) consistent with each other? Explain why or why not.
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