We already know how to calculate the moment caused by a force about a point, O, using the vector formulation, 
M_O equals to r cross F, with r being the position vector from point O to vector F. 
But since F is a vector, it can be resolved into two or even more component force vectors following the parallelogram law.
So if F equals to F_1 plus F_2, then M_O equals to r cross F_1 plus F_2,  and then
following the distributive law, M equals to r cross F_1 plus r cross F_2.
And r cross F_1 is simply the moment caused by the force component F_1 about point O, and r cross F_2 is the moment caused by force 
component F_2 about point O. 
Therefore, we can conclude that the moment caused by a force can be calculated by summarizing 
the moments caused by its component forces about the same point. And this is the principle of moments. 
But why do we care about the principle of moments? We want to use it to help us simplify the calculation of moment. Therefore,
normally if we know the point of action of the force, in this case point A,
we would resolve the force vector into a horizontal component F_x and a vertical component F_y, since this way, 
the moment arms of these two component forces can be quickly determined by the coordinates of 
point A, x and y. And therefore the calculation of the magnitude
of the moment can be easily achieved to be F_x times its moment arm, y,
plus F_y times its moment arm x. Note that the sign will change
to negative if the force causes a clockwise rotational effect instead.
Even better, sometimes we can conveniently resolve the force into one component that is along the direction of r, pointing from point O 
towards point A, and another component that is perpendicular to r,
as shown here.
The advantage is: this way the moment arm of F_1 is simply the magnitude of r, 
or in other words, the distance from point O to point A, which can be easily determined.
And also the moment arm of F_2 is simply zero, in other words, component force F_2 does not create any moment about point O,
because its own line of action passes through point O.
Therefore the total moment can be easily calculated to be M equals to F_1 times r.
Again, positive magnitude indicates counterclockwise rotational effect.
Note that the principle of moments also applies to 3D problems.
It is up to you to decide what is the best way to carry out this principle of moments; what is the best way to resolve 
a force into its vector components so that it can help you simplify your calculation.
And this comes with practice and experience.
In this example we need to determine the total moment caused by the three forces, F_1, F_2 and F_3 about point A.
We have several options in terms of how to solve this problem. We can use the vector formulation that we learned before.
But since this is a 2D problem, using scalar formulation is probably easier and more straightforward.
To use a scalar formulation,
we can choose to apply our knowledge of geometry and determine the moment arms 
d_1, d_2 and d_3 for the three forces respectively, and then use this equation to do the calculation.
However that's probably not the most convenient method.
Instead, let's apply the principle of moments, which means that we will first resolve these forces into components.
Again there are unlimited ways to do that, but from observation,
I decided that it is the most convenient to resolve the forces into their respective horizontal and vertical components.
Again from observation we see that
these two force components do not have moment about point A because their lines of action 
pass through point A. For the remaining four force components,
their moment arms to point A are easy to determine, therefore we can do the calculation
and get to our answer.
You can try to solve this problem using other methods as well and do your own comparison to decide which method is the fastest. 
Again it is always up to you how you want to choose the best method.
