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Consider the vector field F(x, y, z) = (3yz - 1)i + (3xz+2yz²)j + (3xy + 2y³z) k. (a) Calculate curl F and state whether or not F is conservative. (b) Follow Procedure 1 on page 94 of Unit 16 to calculate a potential function U such that F=-grad U. (c) Using the expression for U(x, y, z) that you found in part (b), calculate - grad U and confirm that F = - grad U.

Consider the vector field F(x, y, z) = (3yz - 1)i + (3xz+2yz²)j + (3xy + 2y³z) k. (a) Calculate curl F and state whether or not F is conservative. (b) Follow Procedure 1 on page 94 of Unit 16 to calculate a potential function U such that F=-grad U. (c) Using the expression for U(x, y, z) that you found in part (b), calculate - grad U and confirm that F = - grad U.

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 vector field F(x, y, z) = (3yz - 1)i + (3xz+2yz²)j + (3xy + 2y²z) k. (a) Calculate curl F and state whether or not F is conservative. (b) Follow Procedure 1 on page 94 of Unit 16 to calculate a potential function U such that F=-grad U. (c) Using the expression for U(x, y, z) that you found in part (b), calculate - grad U and confirm that F = - grad U.
Transcribed Image Text:Consider the vector field F(x, y, z) = (3yz - 1)i + (3xz+2yz²)j + (3xy + 2y²z) k. (a) Calculate curl F and state whether or not F is conservative. (b) Follow Procedure 1 on page 94 of Unit 16 to calculate a potential function U such that F=-grad U. (c) Using the expression for U(x, y, z) that you found in part (b), calculate - grad U and confirm that F = - grad U.
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