Question

what is the difference between area and area vector discusse in detail?

Answer 1

The problem is that of Orientability. Intuitively, area is a measure of 2-D surfaces. However many times, one may encounter situations where matter, energy or flux is transmitted across  two regions in the bulk and in such situation, to meaningfully talk about the flow of these fluxes, we need to have a notion of orientation. In such situations we associate a normal vector to the area and treat area itself as a vector. However, this is not possible for all manifolds, e.g: Möbius strip. You can check that Mobius strip has no well defined notion of "inside" and "outside" and so its non-orientable

Answer 2

Answer:

Area as a scalar quantity represents only magnitude in a one dimensional plane but area as a vector represents along with magnitude even the plane(direction) in which it is embedded. ... The direction in which surface is pointing makes the area of that surface a vector quantity.