The structure in Figure $3$ is designed so that three cables $\backslash ($ A C$,$ B D $\backslash )$ and $\backslash ($ B E $\backslash )$ support a rod JAB. Each of the cables is unique. In addition, the rod is pinned to a ball and socket at A$.$ A cylinder of weight $400$ kg is attached to the structure as shown in the illustration. Take tote of the coordinate system and the geometry of the cables and the rod.

$3\mathrm{.}1\mathrm{.}1$ Determine the tension in cables AC$,$ and BD and BE$.($Draw a free body diagram$).$

$3\mathrm{.}1\mathrm{.}2$ Determine the $\backslash (\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$y$\}\backslash )$ and z components of the support reaction force resultant at the ball and socket at $\backslash ($ O $\backslash ).$

$(3)$

Figure $3$: Simple structure or pent roa supportea dy a dall and socket and three cables.