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Question Number 124321 by sogol last updated on 02/Dec/20

$$f(x,y,z)=z^2{yz}^3$$$$A=xzi-y^{2}j+2x^{2}yk$$$$div\left(fA\right)=?$$$$curl\left(fA\right)=?$$

Answered by Ar Brandon last updated on 02/Dec/20

$$\mathrm{div}\left(\mathrm{A}\right)=\mathrm{z}-2\mathrm{y}$$$$\mathrm{gradf}={2\mathrm{xyz}}^3\mathrm{i}+{\mathrm{x}}^2{\mathrm{z}}^3\mathrm{j}+{3\mathrm{x}}^2{\mathrm{yz}}^2\mathrm{k}$$$$\mathrm{div}\left(\mathrm{fA}\right)=\mathrm{fdiv}\left(\mathrm{A}\right)+\mathrm{Agradf}$$

Answered by Dwaipayan Shikari last updated on 02/Dec/20

$$Divergence▽.f(x,y,z)=\frac{\partial f}{\partial x}\hat{i}+\frac{\partial f}{\partial y}\hat{j}+\frac{\partial f}{\partial z}\hat{k}$$$$▽.A=z\hat{i}-2y\hat{j}$$$$▽.f=z^5\hat{j}+5z^{4}y\hat{k}$$

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