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TOT 331 1992 Spring O S3 sum of vectors not zero

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June 9, 2024
vectorgeometryVectors

Problem Statement

Let OO be the centre of a regular nn-gon whose vertices are labelled A1A_1,......, AnA_n. Let a1>a2>...>an>0a_1>a_2>...>a_n>0. Prove that the vector a1OA1→+a2OA2→+...+anOAn→a_1\overrightarrow{OA_1}+a_2\overrightarrow{OA_2}+...+a_n\overrightarrow{OA_n} is not equal to the zero vector.
(D. Fomin, Alexey Kirichenko)
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