1. Apr 19, 2010 #1

   Danish_Khatri

   

   Vectors are drawn from the center of a regular n-sided polygon in
   the plane to the vertices of the polygon. Show that the sum of the
   vectors is zero. (Hint: What happens to the sum if you rotate the
   polygon about its center?)
   
   can any body help me out with this question? and what does the rotation of the polygon have to do with this addition of vectors? I am not able to understand this question at all.

    

   Danish_Khatri, Apr 19, 2010
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3. Apr 19, 2010 #2

   berkeman

   

   Staff: Mentor

   Draw the problem for a 4-sided polygon, and see if it makes sense. Then a 6-sided polygon, etc.

    

   berkeman, Apr 19, 2010
4. Apr 19, 2010 #3

   elect_eng

   

   The hint is asking you to look at the symmetry of the problem. Actually, it is asking you to do more than just rotate the figure. The expectation is that you will realize that there is something very special about rotating by 2pi/n. When you do so, do you have a different problem, or the same problem? The answer to this question can lead you to a very simple and elegant proof that the sum of the vectors is zero.

    

   elect_eng, Apr 19, 2010

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