NOTE: Part a is force$-$couple problem. Part b and c are equilibrium problems.

A force $($F$)$ of $4$ kN is applied at a perpendicular to the structure at point $B$ and a couple $(M_A)$ of $2kNm$ is applied at point $A.$ The beam is supported by a hinge $($pin$)$ at point $O$ and a cable from point C $,$ which is in$-$line with the beam. You may assume that the hinge is at the origin, and you may neglect the thickness and mass of the beam. For this beam, do the following:

a$)$ Replace the force F with an equivalent force couple system at point O$.($Do not worry about the applied couple for this part of the problem, just move F to O $).$ Your answer should be in component form for both the force and the couple.

b$)$ Find the magnitude of the tension $($ T $)$ in the cable at C and the components $($magnitude and direction$)$ of the reaction force at the hinge at and $\{$:$O_y).$

c$)$ Imagine that the cable at C was replaced by simply resting the beam against the wall. Would the system still be able to remain in equilibrium? Why or why not?

All answers should be in the coordinate system provided and use units of kN and m $.$