# Surface Integral (Part 2)

Calculus Level 4

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

If the surface integral of the vector field $$\vec{F}$$ over a unit sphere centered on the origin can be expressed as $$\alpha \pi$$, determine the value of $$\alpha$$.

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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