Question: How can we derive the Triangle Law of Addition of Vectors?

James M Monk answered on 14 Jun 2011:

To add up any two (or more) vectors you have to add the separate components. So if one vector is {x1, y1, z1} and another vector is {x2, y2, z2} then their sum is

{x1 + x2, y1 + y2, z1 + z2}

You can see how you could add a third vector, which would give {x1 + x2 + x3, y1 + y2 + y3, z1 + z2 + z3}