Three point charges q are placed at three vertices of an equilateral triangle of side a.find magnitude of electric force on any charge due to other two.

let us consider the extreme left one,
F(for the top particle)= kq^2/a^2 [cos60.i + sin60.j]
F(for extreme right)= kq^2/a^2.i
net force = kq^2/a^2 [ 3/2.i + root(3) / 2.j]
magnitude= kq^2/a^2.[ root 9/4 + 3/4 ]
= root(3) [kq^2/a^2].ANS

use the concept of r=√a^2+b^2+ 2ab cosΦ    

where the two vetors are a=E b=E DIRECTED AWAY FROM the charge

E=k.q\side^2

which turns out to be √3 E