(a) State a necessary condition for a vector field to be a gradient.(b) Determine if the vector fieldF(x, y) = (²2x - 3y-2x² + y² - 6x - 4y + 13' x² + y² - 4y - 6x +13,is a gradient in its domain.

Given vector field: Fx,y=x-3x2+y2-6x-4y+13,y-2x2+y2-6x-4y+13 To find: a) The necessary condition for…

Answered: (a) State a necessary condition for a…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 13P

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(a) State a necessary condition for a vector field to be a gradient. (b) Determine if the vector field x-3 (a x² + y² - 6x - 4y + 13' x² + y² - 4y - 6x +13, - 6x +13) F(x, y) = is a gradient in its domain. y-2