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Prove that the sum of all the vectors drawn from the centre of a regular octagon to its vertices is the null vector. |
Answer» Solution : Let O be the centre of a regular OCTAGON ABCDEFGH. Then `vec(OA)` = `-vec(OE)`, `vec(OB)` = `-vec(OF)` `vec(OC)` = `-vec(OG)`, `vec(OD)` = `-vec(OH)` Now `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))` = `vec0+vec0+vec0+vec0` = 0 |
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