Consider a ΔABC with D, E and F being the midpoints of sides BC, CA and AB respectively.
Let the position vectors of these vertices and midpoints be as shown in the figure.
We need to prove.
As D is the midpoint of BC, using midpoint formula, we have
Recall the vector is given by
Now, consider the vector.
Thus, the sum of the three vectors determined by the medians of a triangle is zero.
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