Problem $1(16/60)$

Mast $\backslash ($ A B C $\backslash )$ is being supported by a ball$-$and$-$socket joint at base $\backslash ($ A $\backslash )$ and by three cables BE$,$ BG and CD as shown.

a$)$ Draw the free$-$body diagram for mast ABC

b$)$ Write the tensions in cables $\backslash (\backslash$mathrm$\{$BE$\},\backslash$mathrm$\{$BG$\}\backslash )$ and CD in vector form.

c$)$ If the tension in cable CD is $500$ N $,$ determine the tensions in cables BE and BG$.$