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I tried expressing the net electrostatic force on the third particle both on the x-axis and on the y-axis. The net force on both axis is =0. I introduced angles alpha and beta to express the angle between the x-axis and a line from particle 1 or particle 2 to particle 3, respectively. I can find the net electrostatic force using this and the Pythagorean theorem - but the expression has too many unknowns to be solved for x and y of the 3rd particle.

What am I missing here? How should I go about solving this?

Thanks.