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Cylindrical coordinates problem


Hi,
I'm having a hard time understanding how Cylindrical Coordinates work in 
Mathematica.  I have several questions:
1.  What is the expression for unit vectors in Cylindrical Coordinates in 
Mathematica?  For example is this correct: r_unit = {1,0,0}, phi_unit = 
{0,1,0}, and z_unit = {0,0,1}???
2.  How do you perform vector cross product of these unit vectors in 
Cylindrical coordinates in Mathematica?  for example: CrossProduct [ {1, 0, 
0}, {0, 1, 0}] gives = {0, 0, 0} which is not the correct answer, then how 
am I supposed to be doing it?

Can anyone please help?

thanks in advance!


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