# Surface Integral

Calculus Level 4

$\Large{\vec{F} = x(y-z)\hat{\imath} + y(z-x)\hat{\jmath} + z(x-y)\hat{k}}$

Determine the surface integral of the vector field $$\vec{F}$$ over a unit sphere centered on the origin.

Note: $$\hat{\imath}, \hat{\jmath},\hat{k}$$ are unit vectors associated with the three Cartesian coordinate axes ($$x,y$$, and $$z$$ respectively).

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