$[30$ points$]$ Two chains are attached to the panel as shown.

a$)$ Write vec$(F_1)$ as a Cartesian vector

b$)$ Write vec$(F_2)$ as a Cartesian vector

c$)$ Determine the angle theta between lines AC and BC

d$)$ Determine the magnitude of the moment that force $F_2$ causes about point $C.$

e$)$ Determine the moment that vec$(F_1)$ causes about hinge $D.$ Report your answer as a Cartesian vector.

f$)$ Determine the moment that vec$(F_1)$ causes about the hinge edge of the panel $($line ED$).$ Report your answer as a Cartesian vector.