The weightless regular hexagonal object below is attached to a post and fixed to the ground at point $A.$ The fix point is well$-$suited for tensile loading but is much weaker when shears or torques are applied. A$1$ N force directed at $60$ counterclockwise from the $x$ axis is applied at a corner of the hexagon at point B $.$ A spring with Hooke constant $k=5\frac{N}{m}$ and undeformed length $l_0=1m$ is attached at one end to the left corner of the hexagon at point C $.$ Suppose the origin of the plane lies at the center of the hexagon at O $.$

Determine the following:

a$)$ The force vector at point C which would eliminate reaction moments and reaction shear force at the fixed support at point A$.($Shear force acts in the $x$ direction$).$

b$)$ The position of the other end of the spring $($point D$)$ which would apply the force vector determined in part $($a$).$ Note, Hooke's Law: $F=kl.$

c$)$ The reaction force in the fixed support. Is the vertical post in tension or compression?