Let S Be an Oriented Surface with Surface Area 6 $\vec{F}=a \vec{i}+b \vec{j}+c \vec{k}$

Essay

Let S be an oriented surface with surface area 6.Suppose $\vec{F}=a \vec{i}+b \vec{j}+c \vec{k}$ is a constant vector field with magnitude 3.If the angle between $\vec{F}$ and $\vec { n }$ is $\pi$ /6 at each point of the surface S, determine the value of the flux integral $\int_{S} \vec{F} \cdot \overrightarrow{d A}$ .