Let's say that we have a plane in 3 dimensions and that we know 2 vectors that belong in this plane. I want to find a unit vector of this plane. My teacher proceeds to taking the cross product of these 2 vectors and then normalising the resulting vector by dividing it with it's norm.
But..Isn't the cross product of the two vectors, a vector perpendicular to the plane that our 2 initial vectors belong? If a vector is perpendicular to a plane, doesn't that mean that the vector is not in the plane?