Halliday, Resnick & Walker — Gravitation: Problem Problem_15

Three dimensions. Three point particles are fixed in place in an \(xyz\) coordinate system. Particle \(A\), at the origin, has mass \(m_A\). Particle \(B\), at \(xyz\) coordinates \((2.00d, 1.00d, 2.00d)\), has mass \(2.00m_A\), and particle \(C\), at coordinates \((-1.00d, 2.00d, -3.00d)\), has mass \(3.00m_A\). A fourth particle \(D\), with mass \(4.00m_A\), is to be placed near the other particles. In terms of distance \(d\), at what (a) \(x\), (b) \(y\), and (c) \(z\) coordinate should \(D\) be placed so that the net gravitational force on \(A\) from \(B\), \(C\), and \(D\) is zero?