recently I was trying to solve this problem:
If I know 3D position vectors P0 and P1 how would I go about solving for P2 and P3?
I assumed it would be by taking the cross product of the vector P1 - P0 with an arbitrary basis vector like (0,1,0)
Vector3 perpendicularVector = Vector3.Cross((P1-P0), Vector3.Up);
but I wasn't able to make that work.
Any help on why my understanding is flawed and what I need to study to be able to understand a problem like this would be greatly appreciated!