Given a parametric curve $\vec r(t)$ and a vector $\vec v$ (not necessarily a vector that was calculated using the derivatives of $\vec r(t)$ , and not necessarily one that is normalized) what is the best way to find the point(s) on the curve where the tangent vector at that point is parallel to $\vec v$?
I would think you should normalize the input vector and set each component of this vector equal to the "normalised" derivative of each component of the curve, but is there any way to accomplish this without having to normalise vectors? Maybe something to do with dot product?