Is F Path Independent at r=0?

[luju]

Homework Statement

F(r) = r/!r!^3 (Sorry but the ! is supposed to imply that its scalar)

I found the curl using the cartesian coordinate definition of curl. It came out to be zero. Now the question is, is F path independent? Its silly, because if the curl is zero then it does imply that its path independent, however F is not defined when r is zero. So i m confused here. Any help will be deeply appreciated.

 

[Dick]

Since r=0 is the only place that r/|r|^3 is undefined, you can check if it's path independent by checking that the integral around any closed path enclosing r=0 is zero. You can check any particular path you want. If one vanishes, they all do.