Vector3.OrthoNormalize

Since the documentation for this function states that both vectors are normalized and then the second vector is made to be orthogonal to the first (i.e. 90 degrees angle between second and first vector), my question is whether I should even bother with G-S Orthonormalization or just use this:

Vector3 OrthoNormalize( Vector 3 normal, Vector3 tangent )

{

normal.normalize();

tangent.normalize();

return tangent.cross( normal );

}

So is the cross-product of two normalized vectors a third vector that has a 90 degree angle to the first one?