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Calculate the divergence and the curl of this vector function.

Calculate the divergence and the curl of this vector function.

Advanced Engineering Mathematics
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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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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