Alright, so I worked it out and I want to see if I'm on the right track following what you said.
For the function to = <0,0,0>, (u,v) would have to be (0,0). I then found the partials of the function with respect to u and v.
ru(u,v) = vi + e^vj + ve^uk
and
rv(u,v) = ui + ue^vj + e^uk...