Answer
The particles have to be placed (a) on the corners of an equilateral triangle
Work Step by Step
Gravitational force between two particles having masses $M$ and $m$ and separated by a distance $r$ is given by the formula:
$|F|=\frac{GMm}{r^{2}}$
In our case, the masses are identical. If the particles are placed on the corners of an equilateral triangles of side $a$, the distance between them will also be identical.
Another thing is that the forces acting on a particle due to other two make an angle $60^{\circ}$ between them, which is also same for each particle.
Thus, the magnitude of resultant gravitational forces would be same, if the particles are placed on the corners of an equilateral triangles.
