Problem$-3($HL$).$ Diagram below shows top view of a door which is hinged at the left end, and can rotate freely with no friction. The width of the door is $1$ meter, other relevant distances are shown in the diagram in meters. There are three forces applied on the door. $($a$)$ Follow the standard procedure practiced in lecture, sketch briefly and find the perpendicular lever arm $|{)}_{?}$ of force $F$ about the hinge. $($b$)$ Find the value of force $F$ when the door is in equilibrium, by setting up net $=0$ equation. $($Pay attention to the CW CCW sign conventions.$)$