InterviewSolution
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InterviewSolution
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Prove that the sum of threevectors determined by the medians of a triangle directed from the vertices iszero. |
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Answer» Let `O` is the center of regular octagon `ABCDEFGH`. Please refer to video to see the regular octagon. Now, `vec(OA) = -vec(OE)` `vec(OB) = -vec(OF)` `vec(OC) = -vec(OG)` `vec(OD) = -vec(OH)` Now, sum of all vectors drawn from the center of this octagon `=vec(OA)+vec(OB)+vec(OC)+vec(OD)+vec(OE)+vec(OF)+vec(OG)+vec(OH)` `=(vec(OA)+vec(OE))+(vec(OB)+vec(OF))+(vec(OC)+vec(OG))+(vec(OD)+vec(OH))` `=0+0+0+0 = vec0`. Therefore, the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector. |
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