If A 1 , A 2 , A 3 , ......, A n are the vertices of a regular plane polygon with n sides…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If A1, A2, A3, ......, An are the vertices of a regular plane polygon with n sides & O is its centre then\[\sum_{i=1}^{n-1}\left(\overrightarrow{\mathrm{OA}}_{i} \times \overrightarrow{\mathrm{OA}}_{i+1}\right)=\]
- \((1-\mathrm{n}) \overrightarrow{\mathrm{OA}}_{2} \times \overrightarrow{\mathrm{OA}}_{1}\)
- \((n-1) \overrightarrow{\mathrm{OA}}_{2} \times \overrightarrow{\mathrm{OA}}_{1}\)
- \(\mathrm{n} \overrightarrow{\mathrm{OA}}_{2} \times \overrightarrow{\mathrm{OA}}_{1}\)
- none
Answer
(A) (1- n ) OA _ 2 OA _ 1
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