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3. (a) Determine the value of coefficient a for which the vector field F = (ayz + 22, 2.02?, 6ryz² + 2xz) is irrotational that is V x F = 0. (b) Find a potential function for F for the value of the coefficient a determined in item (a). (c) Evaluate the work integral fe F - dr, where C is a path running from the origin to the point (3,1,1).

3. (a) Determine the value of coefficient a for which the vector field F = (ayz + 22, 2.02?, 6ryz² + 2xz) is irrotational that is V x F = 0. (b) Find a potential function for F for the value of the coefficient a determined in item (a). (c) Evaluate the work integral fe F - dr, where C is a path running from the origin to the point (3,1,1).

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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Please solve this vector calculus(vector field and integration) problem. If possible please answer all questions

Thank you.

3. (a) Determine the value of coefficient a for which the vector field F = (ayz³ + z2, 2.xz*, 6ryz² + 2xz) + 2° is irrotational that is V x F = 0. (b) Find a potential function for F for the value of the coefficient a determined in item (a). (c) Evaluate the work integral ſc F · dr, where C is a path running from the origin to the point (3,1,1).
Transcribed Image Text:3. (a) Determine the value of coefficient a for which the vector field F = (ayz³ + z2, 2.xz*, 6ryz² + 2xz) + 2° is irrotational that is V x F = 0. (b) Find a potential function for F for the value of the coefficient a determined in item (a). (c) Evaluate the work integral ſc F · dr, where C is a path running from the origin to the point (3,1,1).
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