Three forces are acting on a $400-$gram ring. vec$(F{)}_1$ is in the $xy-$plane, vec$(F{)}_2$ is in the $yz-$plane, and the coordinate direction $($direction cosine$)$ angles of vec$(F{)}_3$ are ${}_3=120,{}_3=45,$ and ${}_3=60.$

a$.$ Draw the FBD of the ring. Treat the ring as a particle.

b$.$ Write all forces in the FBD as Cartesian force vectors. Leave the magnitudes of $F_1,F_2,$ and $F_3$ as unknown variables but calculate the magnitude of any other force if it is known.