Question

If a vector field A(x,y,z)=xz3ex - 2x2yzey+2yz4ez , calculate the divergence Ñ·A at point M(1,-1,-1).

Answer 1

Gives

$$A(x,y,z)=xz^3 \hat{e_x}+2x^2yz \hat{e_y}+2yz^4 \hat{e_z}$$

$$\nabla.A=(\frac{d}{dx}\hat{e_x}+\frac{d}{dy}\hat{e_y}+\frac{d}{dz}\hat{e_z})(xz^3 \hat{e_x}+2x^2yz \hat{e_y}+2yz^4 \hat{e_z} )$$

$\nabla.A=z^3+2x^2z+8yz^3$