Problem $3$

The following plate is supported by hinges at points A and $B.$ These hinges are on the line $AB$ and are well$-$aligned so that they don't apply a reaction moment to the plate. Both A and $B$ lie in the $y-$z plane. A force $P=4$hat$()-5$hat$()($lb$)$ is applied at $D.$

$142(56)$

A$.$ Find the tension in the cable $CE.($Hint: Consider the moment about axis $AB.)$

B$.$ In this instance, the component of the hinge's reaction force at B along $AB$ is zero $($Hint: You will need to write an equation describing this, on top of your other equilibrium equations$).$ Using your results for Part A $,$ find the reaction forces at the hinges at A and $B.$ You do not need to solve this all the way through; however, you must write all the relevant force and moment equations $($matrix form is okay$)$ that you would need to solve the problem completely. $($If you were unsuccessful in solving Part A$,$ you can instead use the variable $T$ for the tension$).$

C$.$ Using your results for Part A$,$ reduce the tension in cable $CE$ and force $P$ to a wrench system, and find the coordinates for where the line of action would pierce the $x-z$ plane $($not the plate!$).($If you were unsuccessful in solving Part A$,$ please use $T=5lb.)$

A$.$

$M_{AB}=0,r_{AD}P+r_{BC}{T}_{EC}=0$

$\{\begin{array}{ccc}\text{:}[4\text{h}\text{a}\text{t}& (i)+0\text{h}\text{a}\text{t}(j)+0\text{h}\text{a}\text{t}(k)][4\text{h}\text{a}\text{t}(i)-5\text{h}\text{a}\text{t}(j)+0\text{h}\text{a}\text{t}(k)]+\{4\text{h}\text{a}\text{t}(i)+0\text{h}\text{a}\text{t}(j)+0\text{h}\text{a}\text{t}& (k)\}{T}_{EC}=0\end{array}$

$T_{EC}=[-4$hat$(i)+5$hat$(j)+0$hat$(k)](Ib)$

$F_{BZ}=F_{AZ}$

$F_{Ax}+F_{Bx}+P_x=T_x$

$F_{By}+F_{Ay}+T_y=P_y$

$T_z=0$

$2,368T_{CE}-28124sin20T_{CE}$

$T_{CE}=\frac{-20}{2,348-2\mathrm{.}8sin20}$

$=-{142}^2$

B$.$

C$.$

not quite sure about part b n c is it okay for u to plug the number in