Particle 1 carrying (2.0 mu mathrm{C}) of charge is fixed at the origin of a rectangular coordinate

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Particle 1 carrying \(2.0 \mu \mathrm{C}\) of charge is fixed at the origin of a rectangular coordinate system, particle 2 carrying \(-1.0 \mu \mathrm{C}\) is fixed \(45^{\circ}\) above the positive horizontal axis \(2.0 \mathrm{~mm}\) from the origin, and particle 3 carrying \(-1.0 \mu \mathrm{C}\) is fixed \(45^{\circ}\) below the horizontal axis \(2.0 \mathrm{~mm}\) from the origin. Where in the system should you place a particle 4 carrying \(-2.0 \mu \mathrm{C}\) so that the vector sum of the electric forces exerted on particle 1 is zero?

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