Problem $3$:

The rope CE exerts an $800$ N force $T$ on the hinged door. Let $r_{BC}$ be the vector from point B to point C $.$

$1)$ Express $T$ in terms of Cartesian components;

$2)$ Determine the unit vector $n,$ which is perpendicular to the door;

$3)$Find the components of and that are parallel and perpendicular to the door; $($Hint: determine perpendicular to the door first, and think about why?$)$

Determine the product $n*(r_{BC}xT).$

$($Hint: perpendicular to the door also means that it is parallel to the unit vector that is perpendicular to the door. Hope this helps.$)$