f-x-y-z-z-2-yz-3-A-xzi-y-2-j-2x-2-yk-div-fA-curl-fA-

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

f (x, y, z) = z^{2} {y z}^{3}

A = x z i - y^{2} j + 2 x^{2} y k

d i v (f A) = ?

c u r l (f A) = ?

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

div (A) = z - 2 y

gradf = {2 xyz}^{3} i + x^{2} z^{3} j + {3 x}^{2} {yz}^{2} k

div (fA) = fdiv (A) + Agradf

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

D i v e r g e n c e ▽ . 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} - 2 y \hat{j}

▽ . f = z^{5} \hat{j} + 5 z^{4} y \hat{k}