From the question 11th, For N=1(plus or minus) , the magnitude of force vector will be F and direction is the vector itself.
For any other N , the answer will be 0
You get vectors 180 deg. apart , which will cancel each other out( like on positive x axis and negative x axis)
You get vectors which are 120 deg apart, looks something like this ( only see the figure on that page)
But vectors can be displaced , so can also displace it to make a triangle (equilateral triangle) , by doing so you will realize that , by walking along the vector you will end up on same position from where you have started. Which means net vector is 0 .
This theorem is true for all closed shapes like triangle , square, pentagon , hexagon etc.
Vector points towards the vertices of square
Vector points towards the vertices of pentagon
Hexagon ...........so on
Hence the resultant vector will be 0 if it is pointing to the vertices of a symmetric and closed figure