Halliday, Resnick & Walker — Gravitation: Problem 11

11 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?