Please solve this vector calculus(vector field and integration) problem. If possible please answer all questionsThank you. 3. (a) Determine the value of coefficient a for which the vector fieldF = (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 determinedin item (a).(c) Evaluate the work integral ſc F · dr, where C is a path running from theorigin to the point (3,1,1).

Answered: Image /qna-images/answer/0b3655e1-cb20-4976-9105-ed0caf827173.jpg

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).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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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).

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution