In 3D space there are two vectors (A, B) of equal length L, but with different directions.
The beginning points of these vectors are located at a distance of L as well. They could be visualized like this (angles are not equal, both are beginning at the bottom of the image and going up):
A -> \_|/ <-B
I need to determine an angle alpha, by which to rotate vector B around axis Y (Which is given as one of vectors orthogonal to the line between the beginnings of A and B) to reach a situation, where the endings of A and B are also at distance L (Basically to get a 3 dimensional shape from 4 vectors with equal length) If it is hard to calculate an angle, a method for finding coordinates forone of the possible new endpoints for B would also be ok.
The question is:
How can I calculate this angle (one of the two angles), and how can I determine if for given vectors it is even possible to do?