Q. In maths we use area as a scalar quantity but in physics we use area as a vector quantity?? Why so?

Where have you seen it as a vector!

I'm curious about this too...

In physics we use area as a vector quantity to solve numerical

in physics we use area as a vector quantity to solve numerical

We're all curious about this - please give an example of where you have seen an area described by a vector in physics. The closest thing I can think of is that the orientation of a plane surface can be described by its orthogonal vector. But that's not its area. Recall that area has units of square meters and no direction, whereas a vector has a unit of length and a direction.

Yeah, please give a more concrete example. There are certainly plenty of scenarios where one might use a surface integral, integrating over the surface area with respect to some vector normal to that surface, but that's certainly not the same thing as the surface area itself being used as a vector quantity.

We use area as a vector quantity in many places such as
To calculate flux, we say that after doing the dot product of Electric field (vector E) with area (vector A) we get a scalar flux

No - you're not taking the dot product of the electric field and an area, but rather integrating the dot product of the electric field and the surface normal vector over an area:


\Phi _E = \int _S E \cdot dA


Each differential bit of area dA actually has surface area of 0 in the limit but has a normal direction, hence can be expressed as a vector. That is NOT the same thing as saying that area is a vector.

Thanks actually I think my teacher had taught me wrong. Now I will go to him tomorrow and will speak to him about this.