ES80 Moment About A Line 

The moment about a line is defined as shown where  unit vector along the line  moment about any point on the line Note: the moment about the line is a scalar. 
The geometric configuration is shown here... 
where 
The moment about a line may be given in component form as shown here. 
A = (2,3,1) B = (3,1,4) C = (2,1,1) 
For example, if a force is applied at point A and the moment is desired about line BC where A, B and C have coordinates as shown and where distances are in meters and forces are in newtons. 

The moment may be found about any point on a line. Let us consider B. Then

The unit vector points from B to C because it was calculated from 

The moment may be calculated... 
This represents a moment of 5.99 about line BC. The negative sign indicates that the moment is in the opposite direction of , therefore pointing from C to B. 
The moment about a line is important in that it allows us to calculate the torque about a shaft. Since we wish to transmit along the shaft, we would like all of the moment to be about that line. Any moments not about that line are deleterious. 