Question

At the end of lecture 19, Professor Aroux remarks that since F and T are parallel vectors, the dot product is just the length of F. Why is that true?

Answer 1

I, believe he said that it is the length of F.

Answer 2

I know now. That is because T is a unit vector. Recall the equation \[dr/dt=T(ds/dt)\]
the left side is velocity, ds/dt is speed or magnitude, and T is unit vector that specifies direction. Since F and T are parallel and T is unit vector (all entries equal to 1), the dot product is F itself.
Hope that helps