Halliday, Resnick & Walker — Gravitation: Problem 33

33 Three point particles are fixed in position in an $xy$ plane. Two of them, particle $A$ of mass $6.00\text{ g}$ and particle $B$ of mass $12.0\text{ g}$, are shown in Fig. 13-30, with a separation of $d_{AB} = 0.500\text{ m}$ at angle $\theta = 30^\circ$. Particle $C$, with mass $10.0\text{ g}$, is not shown. The net gravitational force acting on particle $A$ due to particles $B$ and $C$ is $2.77 \times 10^{-14}\text{ N}$ at an angle of $-163.8^\circ$ from the positive direction of the $x$ axis. What are (a) the $x$ coordinate and (b) the $y$ coordinate of particle $C$?