PROBLEM $6$

a$)$ The force $F$ acting on the boom ABC at $C$ points in the direction of the unit vector $0\mathrm{.}512$vec$()-0\mathrm{.}384$vec$()+0\mathrm{.}768$vec$(k)$ and its magnitude is $8kN.$ The boom is supported by a ball and socket at A and the cables BD and BE$.$ The collar at B is fixed to the boom. Determine the tensions in the cables and the reactions at $A.$

b$)$ The cables BD and BE can each safely support a tension of $25kN.$ Based on this criterion, what is the largest acceptable magnitude of the force $F?$