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Prove by vector method that the medians of a triangle are concurrent. |
Answer» Solution : Let ABC be a triangle and D,E,F be the mid POINTS of the sides of `triangleABC` Let `veca,vecb` and `vecc` be the position vectors of the points A, B, C. Then the position vectors of D< E, F are `(vecb+vecc)/2, (vecc+veca)/2` and `(veca+vecb)/2` respectively. Let G be the point which divides the median into the RATIO 2:1. Then the position vector of G is `2((veca+vecb)/2+1veca)/(2+1)` i.e. `(veca+vecb+vecc)/3` The summetry of the result shows that the point G also lies on the other TWO medians. HENCE the medians are concurrent. (Proved) |
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