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Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the vector field is not conservative, enter dne.) f(x, y, z) = 6xy2z2i + 4x2yz3j + 6x2y2z2k

Respuesta :

LammettHash
A conservative vector field [tex]\mathbf f[/tex] has curl [tex]\nabla\times\mathbf f=\mathbf0[/tex]. In this case,

[tex]\nabla\times\mathbf f=12xy^2z(1-z)\,\mathbf j+4yz^2(2z-3x)\,\mathbf k\neq\mathbf 0[/tex]

so the vector field is not conservative.

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