Consider three ch

Suppose the given charges are placed as shown in figure

Given that the triangle is equilateral so if O is the centroid of the triangle then,

AO = BO = CO = r

Force on charge Q due to q_1,

Force on charge Q due to q_2,

Force on charge Q due to q_3,

By the principle of superposition, total force on the charge Q is,

Since q₁ = q₂ = q₃

Since the triangle is equilateral hence angle between all the sides is 60^o

So the angle between is 120^o

So they form a triangle of cyclic vectors. Consequently,

Hence

The total force on charge q is zero