Show that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero - Maths - Introduction to Three Dimensional Geometry

Question

Show that the sum of three vectors determined by the medians of
a triangle directed from the vertices is zero

Prabhash Srivastava · Answer

Say that the triangle is ABC The vector given the median from A to
BC is (AC+AB)/2 Similarly, the one from B to AC is (BA+BC)/2, and
the one from C to BA is (CB+CA)/2 Adding these, we get zero since
CB=−BC, etc

Show that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.