$3\mathrm{.}1$ The structure in Figure $3$ is designed so that three cables $AC,BD$ and BE support a rod OAB $.$ 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 note 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 $x,y$ and z components of the support reaction force resultant at the ball and socket at O $.$

$(3)$

Figure $3$: Simple structure of bent rod supported by a ball and socket and three cables.