I need to find unit normal and tangent vectors for an ellipse with major axis ( ) of length and minor axis ( ) of length .
My initial guesses are
These are orthogonal, but lead to incorrect results later so I suspect they're wrong.
"Guesses"? Why guesses? Since your ellipse is , derivating you get a tangent vector and thus a perpendicular vector to this first one is a normal to the ellipse...but you're forgetting, I'm afraid, that these vectors have to be of length 1 !