Vector Algebra sounds intimidating, but it's basically a quick way to estimage forces without doing any calulcations. You do this by drawing arrows in your head, connecting the arrows, and drawing an arrow from the beginning to the end. The relative lengths of the arrows is the relative size of the forces.
Vector algebra is applicable for components like ropes that take tension or compression load but not bending.
The basic steps:
Pick a point to analyze. It is easiest if you pick a point where all forces intersect.
Draw arrows for each force that is acting on that point. Make sure the angles are accurate.
Move one of the arrows so that the start of that arrow is at the end of another arrow. Don't rotate the arrows when you move them.
Extend or shorten the tails of the two arrows that have a free end until they intersect.
Measure or estimate the relative lengths of the arrows.
Multiply the known force by the ratio of arrow lengths to get the other forces.
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