Question

Consider a particle moving along the "twisted cubic," with parametrization r(t)=. Find T, the unit tangent vector, and N, principle unit normal vector, at time t=2.

Answer 1

The unit tangent vector is just the tangent vector (derivative of the vector) divided by it's magnitude (square root of the dot product).

Answer 2

The principle unit normal vector is just the unit tangent vector of the unit tangent vector.