Question

If you have a space curve and you're trying to find a vector n that is always normal to it...You have to take the derivative twice, but do you have to normalize as you go?

Answer 1

you have to find the cross product of the normal and tangent vectors. This is called the binormal vector and is perpendicular to the curve at all points of the curve.

Answer 2

if r(t) is your space curve, the unit tangent vector = r'(t)/(magnitude of r't), the unit normal vector r''(t)/ (magnitude of r''(t)). Once you have those two vectors, then you can produce the cross product for the binormal vector which is what you are looking for. That direction vector will e perpendicular to the space curve at all points.