surface integral is denoted by double integral F.n ds here what is n please explain in detail and?

Question

why do we take n unit vector = -i in yz plane,n= -j in xz plane,what is Gauss' divergence theorem in maths its physical meaning and

Answer 1

n is the normal vector to the surface (oriented outwards) at any given point. Thus, F.n is the component of F projecting outwards at any given point, and the surface integral represents the total outwards flux of F through the given surface.

If the surface is given by a function (x, y, z) = f(s, t), then the tangent plane to the surface at any point has vectors u = (∂x/∂s, ∂y/∂s, ∂z/∂s) and v = (∂x/∂t, ∂y/∂t, ∂z/∂t), and the normal is given by n = u×v.