Figure $6$: Problem $5$

Q$6$: Forces vec$(F{)}_1,$vec$(F{)}_2,$ and vec$(F{)}_3$ act on the structure of figure $6.$ 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 vec$(F{)}_h$ and vec$(F{)}_v.$ We are given that $a=2\mathrm{.}0m,b=3\mathrm{.}0m,c=1\mathrm{.}0m,F_1=20N,F_{2}N,F_3=5\mathrm{.}0$ N$.$ Find:

$($a$)F_h,$

$($b$)F_v,$

$($c$)d.$