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Multivariable Calculus

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Moderate

Conservative Vector Field

MVCALC-4OY1LM

Examine which of the following vector fields are conservative:

$$ \begin{align*} \vec{F} &=\langle y\cos(xy), x\cos(xy)-2y\rangle \quad \text{on }\mathbb{R}^2 \\\ \vec{G} &=\langle z, 1, x\rangle \quad \text{on }\mathbb{R}^3 \\\ \vec{H} &=\langle x^2, 2y, -z^3\rangle \quad \text{on }\mathbb{R}^3 \end{align*}$$

A

$\vec{F}, \vec{G}, \vec{H}$

B

$\vec{F}, \vec{H}$

C

$\vec{G}, \vec{H}$

D

$\vec{G}$

E

None of the above