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player1_1_1

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## Homework Statement

Can a vector field exist in polar/spherical system? is it possible to define line integral in these systems? does it make any sense a vector field defined in polar system, ex. [tex]\vec A\left(r,\varphi\right)=r^3[/tex]? and a line integral from [tex]r_1,\varphi_1[/tex] to [tex]r_2,\varphi_2[/tex] like this [tex]\int\limits_L\vec A\left(r,\varphi\right)\mbox{d}r+r\vec A\left(r,\varphi\right)\mbox{d}\varphi[/tex], where L is a line defined by [tex]r\left(\phi\right)[/tex] equation or [tex]r=r(t),\quad\phi=\phi(t)[/tex]

and for spherical system [tex]\int\limits_L\vec A\left(r,\varphi,\phi\right)\mbox{d}r+r\vec A\left(r,\varphi,\phi\right)\mbox{d}\varphi+r\vec A\left(r,\varphi,\phi\right)\mbox{d}\phi[/tex]?

thanks!