It looks right and it makes sense. The Tangent Vector Function's components are all constants, and therefore it has to have a magnitude of zero, and in order for the PUV to exist, can't be zero. That's the way I'd have proven it...
I was rifling through some USSR problem books (with no solutions!) and I found this one, its really easy, but I was dissatisfied with my proof. I think it can be done with less work.
Prove that the principal normal unit vector, denoted does not exist for a linear function
My proof is, dont look if you dont want to
So the tangent unit vector is
does not exist because there will be a division by zero