(Solved): What are \( \nabla \cdot F \) and \( \nabla \times F \) for the vector field \( \mathbf{F}=2 x y \m ...

What are \( \nabla \cdot F \) and \( \nabla \times F \) for the vector field \( \mathbf{F}=2 x y \mathbf{i}+x e^{y} \mathbf{j}+2 z \mathbf{k} \) ? \[ \begin{array}{l} \nabla \cdot \mathbf{F}=2 x+y^{2} e^{y}+2 z \\ \nabla \times \mathbf{F}=x \mathbf{i}+y \mathbf{j} \end{array} \] \( \nabla \cdot \mathbf{F}=2 x+y x e^{y}+2 \) \[ \nabla \times \mathbf{F}=x e^{y} \mathbf{j}-2 z \mathbf{k} \] \( \nabla \cdot \mathbf{F}=2 y+x e^{y}+2 \) \( \nabla \times \mathbf{F}=\left(e^{y}-2 x\right) \mathbf{k} \) \( \nabla \cdot \mathbf{F}=4+e^{y} \) \[ \nabla \times \mathbf{F}=x y \mathbf{i}+e^{y} \mathbf{j}+z \mathbf{k} \]