Halliday, Resnick & Walker — Gravitation: Problem 49

49 Two dimensions. In Fig. 13-35, three point particles are fixed in place in an xy plane. Particle A has mass \(m_A\), particle B has mass \(2.00m_A\), and particle C has mass \(3.00m_A\). A fourth particle D, with mass \(12.0m_A\), is to be placed near the other three particles. In order for the net force on particle A due to the other three particles to be zero, where should particle D be located? Give (a) the distance from A in terms of \(d\) and (b) the angle relative to the positive direction of the \(x\) axis?