The sum of the three vectors determined by the medians of a triangle directed from the vertices is

Question

Arun · 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.

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The sum of the three vectors determined by the medians of a triangle directed from the vertices is

The sum of the three vectors determined by the medians of a triangle directed from the vertices is

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