Question: Find the vector representing the area of a surface. The magnitude of the vector equals the magnitude of the area; the direction is perpendicular to the surface. Since there are two perpendicular directions, we pick one by giving an orientation for the surface.
The rectangle with vertices (0, 0, 0), (0, 1, 0), (2, 1, 0), and (2, 0, 0), oriented so that it faces downward.