Vector Calculus

A continuously differentiable vector field $\vec{F}(x, y, z)$ defined on a simply connected spatial domain is irrotational if and only if:

Options:

• (A) $\nabla \times \vec{F} = \vec{0}$
• (B) $\nabla \cdot \vec{F} = 0$
• (C) $\nabla^2 \vec{F} = \vec{0}$
• (D) $\vec{F} \cdot \vec{F} = 0$