Let say I have 2 vectors (1,0,0) and (0,2,0), and I want to find a third vector that is orthogonal to both of them. I can do a cross product and get (0,0,2). However, I know there are infinite vector in the following form where that are orthogonal to the other two. My question is what is the difference between the orthogonal vector results from cross product and any other orthogonal vector? Why the cross product gives only 1 specific orthogonal vector? What is the significance of this vector? Thank you!