$(6)$ A window is temporarily held open in the $\backslash (50^\{\backslash$circ$\}\backslash )$ position shown by a wooden prop CD$.$ If $\backslash (\backslash$mathrm$\{$a$\}=0\mathrm{.}8\backslash$mathrm$\{$~m$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$b$\}=1\mathrm{.}2\backslash$mathrm$\{$~m$\}\backslash )$ and the mass of the window is $50$ kg with mass center at its geometric center, determine the compressive force $\backslash ($ F$\_\{$C D$\}\backslash )$ in the prop and all components of the forces exerted by the hinges A and B on the window. Assume that A is a thrust bearing hinge and that hinge B is not. $($Hinge A is capable of exerting force components in the $\backslash ($ x$,$ y $\backslash ),$ and $\backslash ($ z $\backslash )$ directions while hinge B is capable of exerting force components only in the x and y directions$).$