Let $\vec{F}=\left(3 x^{2}+y^{4} \sin x\right) \vec{i}+\left(4 y^{3} \cos x+z\right) \vec{j}-y \vec{k}$

Multiple Choice

Let $\vec{F}=\left(3 x^{2}+y^{4} \sin x\right) \vec{i}+\left(4 y^{3} \cos x+z\right) \vec{j}-y \vec{k}$ Is the value of the line integral of $\vec{F}$ along any loop zero?

A) Yes; the function is a gradient vector field.
B) No; the function is not a gradient vector field.