Written Problem $(30$ points$)$: Four forces are acting on a bracket as shown in the figure. For the $F_2,F_3,$ and $F_4$ forces write in terms of Cartesian components using the given $x$ and $y$ axes. What does the magnitude of force F$1$ need to be such that the overall resultant force on the bracket only has a vertical component $($i$.$e$.$ there is no horizontal component for the resultant$).$