I need to ask a question about vectors and cross product? When you take the determinant on 3 vectors, you calculate and get the volume of that specific shape, correct?
When you take the cross-product of 2 vectors, you calculate and get the area of that shape and you also get the vector perpendicular to the plane, correct?

The absolute value of the determinant having rows the components on Ox, Oy, Oz axis is indeed the volume of the parallelipeped spanned by the 3 vectors.
When you take the cross product you get a vector perpendicular on the plane containing the inial 2 vectors and with direction given by the right-hand rule.
If you take the magnitude of this cross-product you get the area of the parallelogram spanned by the 2 vectors.
So cross-product gives a vector. Area is scalar (magnitude of vector)
