The block shown below is subjected to six forces $($three pairs of coupling forces$).$

a$.$ Compute the resultant moment $($expressed as a Cartesian vector$)$ about point $C$ by summing the moment that each individual force creates about point $C.$

b$.$ Compute the resultant couple$-$moment vector $($expressed as a Cartesian vector$)$ by summing the three moments created by each pair of coupling forces.

c$.$ Explain why the answers to parts $($a$)$ and $($b$)$ are the same.

d$.$ Determine the magnitude of the resultant couple moment found in parts $($a$)$ and $($b$)$ and the coordinate direction angles the vector makes with $x,y,$ and $z$ axes.

$2$