91Ó°ÊÓ

For the following exercises, find the curl of \(\mathbf{F} .\) $$\mathbf{F}(x, y, z)=(x-y) \mathbf{i}+(y-z) \mathbf{j}+(z-x) \mathbf{k}$$

For the following exercises, find the curl of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=x y z \mathbf{i}+x^{2} y^{2} z^{2} \mathbf{j}+y^{2} z^{3} \mathbf{k}$$

For the following exercises, find the curl of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=x y \mathbf{i}+y z \mathbf{j}+x z \mathbf{k}$$

For the following exercises, find the curl of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=x^{2} \mathbf{i}+y^{2} \mathbf{j}+z^{2} \mathbf{k}$$

For the following exercises, find the curl of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=a x \mathbf{i}+b y \mathbf{j}+c \mathbf{k}$$ for constantsa, b, c

For the following exercises, find the divergence of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=x^{2} z \mathbf{i}+y^{2} x \mathbf{j}+(y+2 z) \mathbf{k}$$

For the following exercises, find the divergence of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=3 x y z^{2} \mathbf{i}+y^{2} \sin z \mathbf{j}+x e^{2 z} \mathbf{k}$$

For the following exercises, find the divergence of \(\mathbf{F}\) $$\mathbf{F}(x, y)=(\sin x) \mathbf{i}+(\cos y) \mathbf{j}$$

For the following exercises, find the divergence of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=x^{2} \mathbf{i}+y^{2} \mathbf{j}+z^{2} \mathbf{k}$$

For the following exercises, find the divergence of \(\mathbf{F}\) $$\mathbf{F}(x, y, z)=(x-y) \mathbf{i}+(y-z) \mathbf{j}+(z-x) \mathbf{k}$$