Solve the following two problems:

In the system shown on the right, a door is supported by hinges at points A and $B$ and by a chain $CD.$ Determine the following:

a$.$ the unit vector from $C$ to $D$;

b$.$ the cartesian form of the force $F$;

c$.$ the moment of the $80lb$ force about $B$; and

d$.$ the magnitude of the moment you determined in part $\text{'}c\text{'}.$

The force of $F=\{-21\mathrm{.}4i+42\mathrm{.}8j-64\mathrm{.}1k\}|b|$ acts along the edge DB of figure below.

a$.$ Determine the magnitude of the moment of this force about the edge AC $($use position vector AD for the second row of your matrix$).$

b$.$ For this part, use position vector $CD$ in your calculation instead of position vector $AD$ and calculate the magnitude of the moment of this force about the edge $AC.$

c$.$ Compare your answer for part $\text{'}$a$\text{'}$ and $\text{'}$b$\text{'}$ and explain your results.