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If a vector field $\vec{F}$ is path independent then...

$\int_C \vec{F} \cdot ds = 0$ for any curve $C$.

$\int_C \vec{F} \cdot ds = 0$ for any simple closed curve $C$.

$\int_C \vec{F} \cdot ds = V(P) - V(Q)$ for potential function $V$ and curve $C$ from points $P$ to $Q$.

$\vec{F}$ is conservative.

None of the Above