Area is a scalar quantity. But in some of the problems it is convenient to treat it a a vector. The question is how to associate a vector to the area of a curved surface. Let us divide the given closed area into a large number of very small area elements. Each small area element may be treated as planar. As normal to the plane specifies the orientation of the place, therefore, the direction of a planar area vector is along its normal. But a normal can point in two directions, inwards or outwards. By convention the vector associated with every area element of a closed surface is taken to be in the direction of the outward normal.
Thus, an area element vector ΔS at a point on a closed surface can be written as
Where ΔS in magnitude of the area element and `n is a unit vector in the direction of outward normal at that point.
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