Understanding Vector Addition in Regular Polygons

[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 anybody 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.

 

[berkeman]

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 anybody 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.

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

 

[elect_eng]

... what does the rotation of the polygon have to do with this addition of vectors?

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.