What is div and curl of the vector field (3x^2z+ye^x)i+(e^x) j+(x^3) k? Is the vector field conservative?

Question : Calculate the div and curl of the vector field \[F\left(x,y,z\right)=(3x^2z+ye^x)\hat{i}+(e^x)\hat{j}+ (x^3)\hat{k}\] Is the vector field conservative?Solution :(a) To Find Div (divergence) of the Vector Field \[F\left(x,y,z\right)=(3x^2z+ye^x)\hat{i}+(e^x)\hat{j}+ (x^3)\hat{k}\] Div of Vector Field F(x,y,z) is given as \[\nabla.\ F=\left(\hat{i}\frac{\partial}{\partial x}+\hat{j}\frac{\partial}{\partial…

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