Question involving vectors
I'm not sure where this goes so I've put it here as well as in the geometry section, as the question is part of a set titled "vector calculus".
Air is flowing with a speed of 0.4m/s in the direction of the vector (-1, -1, 1). Calculate the volume of air flowing per second through the loop which consists of straight lines joining, in turn, the following (1,1,0), (1,0,0), (0,0,0), (0,1,1), (1,1,1) and (1,1,0).
I've tried doing this by dot producting he velocity vector with the surface area vector of three planes, a square of area 1 in the xy plane, the same in the xz plane and a triangle in the zy plane of area 0.5. However I don't think this is right. Please help!