Let $\vec { G }$ Be the Constant Vector Field $a \vec { i } + b \vec { j } + c \vec { k }$

Essay

Let $\vec { G }$ be the constant vector field $a \vec { i } + b \vec { j } + c \vec { k }$ .
Find a condition on a, b and c such that $\int_{S} \vec{F} \cdot \overrightarrow{d A}=0$ for any surface S lying on the plane -5x + 3y - 2z = 1.