1. The problem statement, all variables and given/known data Hello. I am relatively new to this subject please forgive my incompetence. Please correct me if I have misunderstandings. I understand that the cross product of two vectors (say A and B) in R3 is a vector that is orthogonal to both A and B. But how A x B be orthogonal to the plane spanned by A and B? I don't understand what this plane spanned by A and B should look like geometrically. Wouldn't A x B be parallel to the plane spanned by A and B?