Let $S$ be the part of the cylinder $x^{2}+y^{2}=1$, whichis in the first octant of space $(x \geq 0, y \geq 0, z \geq 0$ and below the plane $z=6$. Moreover $5$ has the outward orientation. a) Provide the Parametric equations for $S$, the vector function for , their Domain $D$ and the unit normal vector $\vec{n}$ which determines orientation of $5$. b) Find the value of the Flux of the vector field $\vec{F}$ across that surface, $$ \iint_{S} \vec{F} \cdot loverrightarrow{d s} $$ where "( (tint) : you can use the fact that for the cylinder $x^{2}+y^{2}=1$, $\underset{r_{0}}{ ightarrow} x \overrightarrow{r_{z}}=\langle\cos (\theta), \sin (\theta), O angle$. CS.VS. 1648