The very first thing we need to know about moment calculation is that moment is always calculated with respect to a certain axis, 
and therefore a force causes different moments about different axes. 
In a 2D problem it always looks like the force is creating a moment about a point, not about an axis.
For example,
in a 2-D plane shown here, when a force is creating a moment about a point O, it is in fact 
creating a moment vector along the positive z axis, as shown in this side view demonstration.
In the 2-D plane, the moment vector can not be visualized, but you can imagine it to be  
the head of an arrow shooting out of the plane, represented by a dot.
The rotational effect is counterclockwise, and the magnitude of the moment is positive.  
If we reverse the direction of the force in this image, then intuitively we can tell the force is now creating a clockwise rotational effect 
about point O. However, the moment that the force creates now points towards the negative z direction, 
still following the right hand rule.
And although from the top view you see a clockwise rotational effect, it is still 
counterclockwise about the moment vector M_z. 
So in the 2-D plane, you should imagine the moment vector as an arrow shooting into the plane, and you can only see the tail of the arrow.
Because of the negative z direction of the moment vector, it is called to create a negative moment.
With that understood, when we calculate the moment caused by a force F about a point O in a 2-D plane, if the force creates 
a counterclockwise rotational effect about point O, the moment, M_O, equals to positive F times d. 
And if the force creates a clockwise effect about point O, 
the moment M equals to negative F times d. In each case, d is the moment arm, which is the 
perpendicular distance from point O to the line of action of force F. 
Or we can just draw a line from point O to anywhere on the line of action of force F, 
r_1, or r_2, or r_3, and determine the angle between each of these three lines and the force, 
theta 1, theta 2, and theta 3 respectively. 
And the moment can be determined to be
F times r_1 sine theta 1, or F times r_2 sine theta 2, or F times r_3 sine theta 3. According to trigonometry,
we know that r_1 sine theta 1 equals to d, so as r_2 sine theta 2 and r_3 sine theta 3.
Resultant moment caused by multiple forces can be determined by simply adding up the individual moment
caused by each force about the same point. Like in this example, 
the total moment about point O equals to F_1 times its moment arm, d_1, plus F_2 times d_2, minus F_3 times d_3. 
Note that it’s minus F_3 d_3 because F_3 is creating a clockwise rotational effect about point O. 
