$3-$D Equilibrium

Rigid bar ABCD, supporting a mass at point $C,$ lies in the $x-y$ plane and is supported by a Ball$-$and$-$Socket at points A and $D$ and cable $BE.$

$3.$ Sketch a Free Body Diagram of Rigid Bar ABCD.

$.s($:$-\mathrm{.}394$hat$(i)-\mathrm{.}512$hat$()+\mathrm{.}768$hat$(k)$:$)$

$(-1)$

$4.$ Express the tension in cable BE$,\frac{?}{\text{b}\text{a}\text{r}}(T{)}_{BE}$ as a Cartesian Vector. $($Hint: Position Vector $$ Unit Vector $$ Cartesians$)$

a$.0\mathrm{.}384T_{B{E}^{\frac{?}{\text{b}\text{a}\text{r}}(1)}}+0\mathrm{.}512T_{B\frac{E}{b}ar()}+0\mathrm{.}768\frac{T_{BE}}{b}ar(k)$

b$.-0\mathrm{.}384\frac{T_{BE}}{b}ar(1)-0\mathrm{.}512T_R$

c$.-0\mathrm{.}384\frac{T_{BE}}{b}ar(1)-\frac{0\mathrm{.}768}{b}ar()+0\mathrm{.}512\frac{T_{BE}}{b}ar(k)$

d$.-0\mathrm{.}384\frac{T_{BE}}{b}ar(1)+0\mathrm{.}512$ T$.i($Hint: Dot Product$)$

a$.7570N-m$

c$.7270N-m$

d$.7870N-m$

$6.$ Determine the magnitude of the force in cable BE$.($Hint: Dot Product$)$

a$.4\mathrm{.}39kN$

$16.459kN$

c$.4\mathrm{.}99kN$

d$.4\mathrm{.}79kN$