Find the flux of the field $\displaystyle \mathbf{F}$ across the portion of the sphere $\displaystyle x^2+y^2+z^2=a^2$ in the first octant in the direction away from the origin, where $\displaystyle \mathbf{F} = y\mathbf{i} -x\mathbf{j} + \mathbf{k}$

I get:

Flux = $\displaystyle \displaystyle \int_S \mathbf{F} . \mathbf{n} d\sigma = \int_R \mathbf{F}. \frac{\pm \bigtriangledown g}{\bigtriangledown . \mathbf{p}} dA$

$\displaystyle \bigtriangledown g = 2x\mathbf{i}+2y\mathbf{j}+2z\mathbf{k}$

But i cannot find what is the right $\displaystyle \mathbf{p}$