Suppose that are the sides of the triangle.
Then in some order we would have .
Notice that .
"In a triangle, let u, v, and w be the vectors from each vertex to the midpoint of the opposite side. Use vector methods to show that u + v + w = 0."
I found an answer to the problem here, but I am still confused. Could someone explain the logic in a little more detail?
Forgive me, I may have forgotten (or never learned) the rule that is be critical to this problem. Is it a generally understood fact that the vector sum of the sides of a triangle is 0 (i.e. this is not something that I would have to prove in my answer)?