Question

Convert the vector A = xy ax - 2x ay to cylindrical system

Answer 1

Answer

In cylindrical coordinate system

$x=\rho cos\phi \\y=\rho sin\phi \\z=z$

And also

$a_x=cos\phi a_\rho -sin\phi a_\phi$

$a_y=sin\phi a_\rho +cos\phi a_\phi$

So vector

 A = xy a_x - 2x a_y

Putting all value we get

$A=(\rho cos\phi-2) \rho^2sin\phi cos\phi a_\rho-(\rho sin^2\phi+2cos\phi) \rho cos\phi a_\phi$