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Question Number 170015 by Best1 last updated on 14/May/22
verify that the force    F=xyi+xyj+yzk is   conservative
$${verify}\:{that}\:{the}\:{force}\: \\ $$$$\:{F}={xyi}+{xyj}+{yzk}\:{is} \\ $$$$\:{conservative} \\ $$
Answered by ajfour last updated on 14/May/22
dW=xydx+xydy+yzdz  2dW=yd(x^2 )+xd(y^2 )+yd(z^2 )            =yd(x^2 +z^2 )+xd(y^2 )        =yd(s^2 −y^2 )+xd(y^2 )  ....!!
$${dW}={xydx}+{xydy}+{yzdz} \\ $$$$\mathrm{2}{dW}={yd}\left({x}^{\mathrm{2}} \right)+{xd}\left({y}^{\mathrm{2}} \right)+{yd}\left({z}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:={yd}\left({x}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)+{xd}\left({y}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:={yd}\left({s}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)+{xd}\left({y}^{\mathrm{2}} \right) \\ $$$$….!! \\ $$

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