In Problem, use vector methods to prove the given theorem.The medians of a triangle are co...

In Problem, use vector methods to prove the given theorem.

The medians of a triangle are concurrent at a point two-thirds of the way from each vertex to the midpoint of the opposite side. [Hint: Let  and  (see Figure 2.33) and use the result of Problem.]

Figure 2.33

Problem

Show that if neither u nor v is a scalar multiple of the other and au + bv = 0, then a = b = 0.