Answer :

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 q_{1} = q_{2} = q_{3}

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

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