Vector Representation  Force Couples
Moment about an Axis: Consider the force passing through point A as shown in the figure.
The view from the y axis reveals that is perpendicular to the x axis and that its line of action does not intersect the x axis. Therefore, the moment of about the x axis is found as where is the moment arm of the force with respect to the x axis. In this case, the moment axis is pointing in the positive x direction as shown. Similarly, the view from the x axis reveals that is perpendicular to the y axis as well. Hence, the moment of about the y axis is found as 

where is the moment arm of the force with respect to the y axis. In this case, the moment axis is pointing in the negative y direction. Also as to be expected, since is parallel to the z axis. 
We can now expand this discussion to the case of calculating the moment about an arbitrary line aa. Two commonly encountered cases are described next.