3. (40 pts.) A particle travels from ($-\frac{1}{3}$,1,-2) to (9,9,6). Its motion is described by the
position function \(\vec{r}(t) = \langle \frac{t^3}{3}, t^2, 2t\rangle\).
a) Find the distance the particle travels along the path, its average speed, and its
displacement [the distance it could have traveled if in a straight line].
b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by
time) including curvature and torsion.