The horizontal rectangular plate with shown dimensions weighs $0\mathrm{.}7kN$ and it is supported by a cable system as indicated. Assume that the weight of the plate acts in the center of the plate. Determine the tensions $T_O$ in cable $OA,T_B$ in cable $AB$ and $T_C$ in cable $AC.$ Point A lies $1\mathrm{.}2m$ above the horizontal $xy-$plane. Complete the cartesion vector form for the forces $\frac{?}{\text{b}\text{a}\text{r}}(T{)}_O\frac{,}{b}ar(T{)}_B$ and $\frac{?}{\text{b}\text{a}\text{r}}(T{)}_C$ that the respective cables $AO,$

$AB$ and $AC$ exert on particle $A.$

$\frac{?}{\text{b}\text{a}\text{r}}(T{)}_O=T_O\{\frac{,}{b}ar(i)+\frac{,}{b}ar(j)+\frac{,}{b}ar(k)\}\frac{?}{b}$

$ar(T{)}_B=T_B\{\frac{,}{b}ar(i)+\frac{,}{b}ar(j)+\frac{,}{b}ar(k)\}\frac{?}{b}$

$ar(T{)}_C=T_C\{\frac{,}{b}ar(i)+\frac{,}{b}ar(j)+\frac{,}{b}ar(k)\}$

Solve the system of equilibrium equations and give the final answers for the tensions in the cables.

Tension in cable $AO$ has magnitude

$kN.$

Tension in cable $AB$ has magnitude

$kN.$

Tension in cable $AC$ has magnitude

$kN.$