Problem $1$: Equivalent Systems $(25\%)$

Saruman has set his Uruk$-$hai to work building war machines for his assault on Helm's Deep. Realizing that he would rather have them fighting than building, Saruman decides to replace the efforts of the $4$ Uruk$-$hai with one cave troll, each one exerting a force $(F_1,F_2,F_3,F_4)$ on the machine. Determine the magnitude, direction, and location of the equivalent force that the cave troll must exert on the arm to achieve an equivalent loading on the machine.

Take:

$F_1=100lb$

$F_2=150lb$

$F_3=260lb$

$F_4=80lb$

$a=6ft$

$b=2ft$

$c=4ft$

$d=3ft$

$=30$