Unit vector in cylindrical coordinates

[JasonHathaway]

Hi everyone,

I've two vectors in cylindrical coordinate - $(-1,\frac{3\pi}{2},0),(2,\pi,1)$ - and I want to find the perpendicular unit vector of these two vector.

Basically I'll use the cross product, then I'll find the unit vector by $\hat{u}=\frac{\vec{u}}{||\vec{u}||}$.

But do you I have to convert the vector to the cartesian coordinates?

 

[coquelicot]

You can perform the cross product directly in cylindrical coordinates. Explicit formulas can be found easily in the web (I believe), or you can derive the formulas by yourself: Simply write down the relations that express the cartesian coordinates in term of the cylindrical coordinates, and then substitute the cylindrical coordinates in the expression of the cross product in cartesian coordinates.