Q:

Unit vector of a plane

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?

A:

Yes you are right, the unit vector obtained by the cross product is orthogonal to the plane but maybe that was exactly what your professor was looking for (otherwise we could simply normalize one of the two given vectors).

