Problem Statement:

A rigid rectangular plate is subjected to two couple forces acting in $3$D space:

Couple $1$:

A pair of forces, each with a magnitude of $F_1=120N,$ acts in opposite directions at points $A(2,-1,0)$ and $B(5,3,0).$ These forces are parallel to the $xz-$plane, with the line of action along the vector $u_1=3i+4k.$

Couple $2$:

Another pair of forces, each with a magnitude of $F_2=180N,$ acts in opposite directions at points $C(1,2,4)$ and $D(1,5,7).$ The forces are parallel to the $yz-$plane, with the line of action along the vector $u_2=3j+3k.$ Therefore, determine the forces and resultant moments of these two couples about the origin $O(0,0,0).$