Hey cyhui.

This reminds of frenet frame considering of a normal vector, a bi-normal and a tangent vector and these things are discussed in curved geometries. Take a look at this:

Frenet

You'll notice that there are expressions for Tangent, Normal, and Bi-Normal vectors and all you have to show is that the Tangent vector is non-zero. You have a non-zero normal vector which means that the Bi-Normal and Tangent Vectors are also non-zero.