The plate shown is supported by two hinges and a cable. The plate has a weight of $100$ lb

acting at the center of gravity $G.$ The hinge at A resists forces in the $y$ and $z$ directions. The

hinge at $B$ resists forces in $x,y,$ and $z$ directions. Determine the vertical reaction $A_z.$

$($a$)-462\mathrm{.}5$ lb

$($b$)-350$ lb

$($c$)512\mathrm{.}5$ lb

$($d$)757\mathrm{.}5$ lb