If a vector field $ \displaystyle{} \vec{V}$ is related to another vector field $ \displaystyle{} \vec{A}$ through $ \displaystyle{} \vec{V}=\nabla \times \vec{A}$, which of the following is true ? Note: $C$ and $S_{C}$ refer to any closed contour and any surface whose boundary is $C$.
- $ \displaystyle{} \oint_{C} \vec{V} \cdot \overrightarrow{d l}=\int_{S_{C}} \int \vec{A} \cdot \overrightarrow{d S}$
- $ \displaystyle{} \oint_{C} \vec{A} \cdot \overrightarrow{d l}=\int_{S_{C}} \int \vec{V} \cdot \overrightarrow{d S}$
- $ \displaystyle{} \oint_{C} \nabla \times \vec{V} \cdot \overrightarrow{d l}=\int_{S_{C}} \int \nabla \times \vec{A} \cdot \overrightarrow{d S}$
- $ \displaystyle{} \oint_{C} \nabla \times \vec{A} \cdot \overrightarrow{d l}=\int_{S_{C}} \int \vec{V} \cdot \overrightarrow{d S}$