A crate on a frictionless floor is pulled by three forces and remains at rest. Two of the forces are $
\vec{F_1}=120\,\text{N}dueeastand\vec{F_2}=80\,\text{N}duenorth.Determinethemagnitudeanddirectionofthethirdforce\vec{F_3}$ that keeps the crate in equilibrium. Express the direction as an angle south of west.