$(25$ pts $)$ The $12-ft$ boom $AB$ has a fixed end $A.$ A steel cable is stretched from the free end $B$ of the boom to a point $C$ located on the vertical wall. If the tension in the cable is $200$ lb $,$ determine, using the cross$-$product, the moment about $A$ of the force exerted by the cable at $B.$

$M=$vec$(r)$vec$(F)$

$A($:$0,0,0$:$)$

$B($:$12ft,0,0$:$)$

$C($:$8ft,4\mathrm{.}8ft,0$:$)$