Answer to Question #314543 in Vector Calculus for Jyo

Question #314543

Determine whether 𝐹 is conservative vector field. If so, find a potential


function for it is


f(x,y,z)=x^yi+5xy^2j


1
Expert's answer
2022-03-21T15:28:13-0400

"f\\left( x,y,z \\right) =x^yi+5xy^2j\\\\rot\\left( f \\right) =\\left| \\begin{matrix}\ti&\t\tj&\t\tk\\\\\t\\frac{\\partial}{\\partial x}&\t\t\\frac{\\partial}{\\partial y}&\t\t\\frac{\\partial}{\\partial z}\\\\\tx^y&\t\txy^2&\t\t0\\\\\\end{matrix} \\right|=\\left( y^2-x^y\\ln x \\right) k\\ne 0"

The field is not conservative.


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