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Question

If G denotes the centroid of ∆ABC, then write the value of GA+GB+GC.

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Solution

Let a, b, c be the position vectors of the vertices A, B, C respectively. Then, the position vector of the centroid G is a + b + c3
Thus,
GA + GB + GC = a - a + b + c3 + b - a + b + c3 + c - a + b + c3 = a + b + c - 3 a + b + c3 = a + b + c- a + b + c = 0

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