Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem 30

30 Forces $\vec{F}_1, \vec{F}_2,$ and $\vec{F}_3$ act on the structure of Fig. 12-35, shown in an overhead view. We wish to put the structure in equilibrium by applying a fourth force, at a point such as $P$. The fourth force has vector components $F_h$ and $F_v$. We are given that $a = 2.0\text{ m}, b = 3.0\text{ m}, c = 1.0\text{ m}, F_1 = 30\text{ N}, F_2 = 10\text{ N},$ and $F_3 = 5.0\text{ N}$. Find (a) $F_h$, (b) $F_v$, and (c) $d$.