How to find the unit vector in cylindrical coordinates

[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?

 

[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.

 

[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?