Divergence and Curl of Unit Vectors?

[cranincu]

Homework Statement

http://img4.imageshack.us/img4/4218/divergenceandcurl.jpg

The Attempt at a Solution

Totally confused on what the question's asking. Wouldn't the divergence of say x_hat be the partial of x_hat over x which is just 0? So every answer would just be 0 or something? Same thing goes with the curl? Thanks

 

[nicksauce]

In cartesian coordinates yes,

But, for example, the r_hat in polar coordinates, written in cartesian coordinates, is
r_hat = (x/sqrt(x^2 +y^2), y/sqrt(x^2 + y^2), 0)

which perhaps has a non-trivial divergence and curl.

 

[cranincu]

oh i get it

edit: wait, not really. How can I make theta or phi into into something like r and z in cylindrical?