Let

vec(F)(x,y,z)=(:x^(2),xy,xz:)

. Let

S

be the part of the plane

6x+3y+2z=6

in the first octant.\ Let

vec(N)

be the upward unit normal vector to the surface

S

. Find the flux of

vec(F)(x,y,z)

through\ the surface

S

.

Let F(x,y,z)=x2,xy,xz. Let S be the part of the plane 6x+3y+2z=6 in the first octant. Let N be the upward unit normal vector to the surface S. Find the flux of F(x,y,z) through the surface S