A Question about Unit Vectors of Cylindrical Coordinates

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sams
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I wrote the equations of the Nabla, the divergence, the curl, and the Laplacian operators in cylindrical coordinates ##(ρ,φ,z)##. I was wondering how to define the direction of the unit vector ##\hat{φ}##. Can we obtain ##\hat{φ}## by evaluating the cross-product of ##\hat{ρ}## and ##\hat{z}## or by using the right-hand rule?

Thank you so much for your help...
 

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  • #2
PeroK
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I wrote the equations of the Nabla, the divergence, the curl, and the Laplacian operators in cylindrical coordinates ##(ρ,φ,z)##. I was wondering how to define the direction of the unit vector ##\hat{φ}##. Can we obtain ##\hat{φ}## by evaluating the cross-product of ##\hat{ρ}## and ##\hat{z}## or by using the right-hand rule?

Thank you so much for your help...
It's all here:

http://mathworld.wolfram.com/CylindricalCoordinates.html

##\phi## (or ##\theta## to mathematicians) is usually defined to be anti-clockwise looking down the z-axis.
 
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sams
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Thank you @PeroK for your help
 

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