So, I'm aware that there is a formula to calculate the distance from center to edge of an ellipse. My problem, however, is in three dimensions. I can formulate it thusly (english is not my first language, keep in mind):
I have an ellipsoid in cartesian space defined by three orthogonal axes 'a', 'b' and 'c'. The ellipsoid can be rotated in any way in relation to the regular cartesian basis vectors. The center of the ellipsoid is in the origin.
The 3d vector 'V' will be defined as a vector with any orientation and given length |V| such that it will precisely reach the edge of the ellipse, starting at the origin.
How do I calculate |V|, given an orientation of 'V'?