Q. 25.0( 1 Vote )

# Show that the sum

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 Similarly, and .

Recall the vector is given by  Similarly, and Now, consider the vector . But , and      Thus, the sum of the three vectors determined by the medians of a triangle is zero.

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