Let $\vec { F } = - 2 \vec { i } - 5 \vec { j } + 4 \vec { k }$

Essay

Let $\vec { F } = - 2 \vec { i } - 5 \vec { j } + 4 \vec { k }$ , and let S₁ be a horizontal rectangle with corners at (0,0,1), (0,2,1), (3,0,1)and (3,2,1), oriented upward; S₂ a rectangle parallel to the xz-plane, with corners at (1,3,1), (2,3,1), (1,3,5)and (2,3,5), oriented in the positive y-direction, and S₃ a rectangle parallel to the yz-plane, with corners at (1,2,1), (1,4,1), (1,2,5)and (1,4,5), oriented in the negative x-direction.
Arrange $\int _ { S _ { 1 } } \vec { F } \cdot \overrightarrow { d A }$ , $\int_{S_{2}} \vec{F} \cdot \overrightarrow{d A}$ and $\int _ { S _ { 3 } } \vec { F } \cdot \overrightarrow { d A }$ in ascending order.