# How to find the unit vector in cylindrical coordinates

1. May 30, 2010

### teslajet

So i'm trying to find out what the procedure is to convert a cartesian unit vector to a cylindrical unit vector. Any thoughts?

2. May 30, 2010

### Jerbearrrrrr

The cylindrical unit vector is er.
x/|x|
Where x is where ever we are. (not cartesian x)

x=r(e_r)+z(e_z)
and |x|^2 = x.x

I think that works. Sorry about not underlining vectors.

e_r can be expressed in terms of e_x and e_y and some trig things.

3. May 30, 2010

### teslajet

Here is my understanding,

Given a unit vector A = x1,y1,z1 in cartesian, to transform into cylindrical just use the transform
A . $$\rho$$
A . $$\phi$$
Z(cartesian)=Z(cylindrical)

my question is, since x . $$\rho$$ = cos$$\phi$$, is the $$\phi$$ that I am supposed to use the tan^-1(y1/X1)?

If this is the case then I don't understand what the solutions manual did with the following problem

I understand part a.) but in part b.) they use 70 degrees as $$\phi$$ when according to part a.), $$\phi$$ should be -89 degrees. Am I missing something?