$2$

A chain is attached to a sewage door, which is used to open it when needed. A force of $80$ N is usually applied along the chain $CD.$

a$.$ Find the position coordinates for the points A$,$ C and D$.[4$marks$]$

b$.$ Calculate the unit vector for the line CD and thus find the Force in Cartesiant$-$vector form. $[6$marks$]$

c$.$ Calculate the relevant position vector and find the Moment of the force about the door hinge at point A$,$ expressing your answer in Cartesian vector form. $[6$marks$]$

d$.$ Calculate the Moment of the force about the door hinge AB $.[4$marks$]$