Problem $1$: A flag pole is fixed to the outside of a downtown brewery in the configuration shown.

$($a$)$ Determine the position vector $r_{AB}$ of cable $AB.$

$($b$)$ Determine the position vector $r_{AC}$ of cable $AC.$

$($c$)$ Determine the position vector $r_{OA}$ of the flagpole $OA.$

$($d$)$ Determine the force vector $F_{AB}$ due to the tension in cable $AB.$