Multivariable Calculus

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Moderate

Which Vector Field is not Path Independent?

MVCALC-KG4CGO

Which of these vector fields is not path independent?

A

$\vec{F}(x,y) = \langle x, y \rangle$.

B

$ \vec{F}(x,y) = \left\langle \frac{x}{x^2+y^2}, \frac{y}{x^2+y^2} \right\rangle $.

C

$ \vec{F}(x,y) = \left\langle \frac{x}{\sqrt{x^2+y^2}}, \frac{y}{\sqrt{x^2+y^2}} \right\rangle $.

D

$ \vec{F}(x,y) = \left\langle \frac{y}{\sqrt{x^2+y^2}}, \frac{-x}{\sqrt{x^2+y^2}} \right\rangle $.

E

None of the Above