$(4)$ A door is supported by hinges at A and $B,$ and by cord CE$,$ as shown,

and a $4611$ force is exerted on it at D$.($This force is purely in

the $-x$ direction.$)$ Hinge $A$ is able to prevent translation in the $y$ direction,

but Hinge $B$ is not able to do that. Find

$($a$)$ the reactions at A and $B$

$($b$)$ the tension in the cord $($magnitude$)$

Hint: Since there are two hinges, neither one needs to prevent rotation about

axes parallel to the $x$ or $z$ axes.