If A 1 , A 2 , A 3 , ......, A n are the vertices of a regular plane polygon with n sides…

Mathematics · JEE Advanced · NTA ExamsThree Dimensional Geometry

If A1, A2, A3, ......, An are the vertices of a regular plane polygon with n sides & O is its centre then\[\sum_{i=1}^{n-1}\left(\overrightarrow{\mathrm{OA}}_{i} \times \overrightarrow{\mathrm{OA}}_{i+1}\right)=\]
  1. \((1-\mathrm{n}) \overrightarrow{\mathrm{OA}}_{2} \times \overrightarrow{\mathrm{OA}}_{1}\)
  2. \((n-1) \overrightarrow{\mathrm{OA}}_{2} \times \overrightarrow{\mathrm{OA}}_{1}\)
  3. \(\mathrm{n} \overrightarrow{\mathrm{OA}}_{2} \times \overrightarrow{\mathrm{OA}}_{1}\)
  4. none

Answer

(A) (1- n ) OA _ 2 OA _ 1

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