Show that moment of a couple does not depend on the point about which you take the moments.

Explanation

Consider a couple as shown in figure acting on a rigid body. The forces `vecF and -vecF` act respectively at points B and A. These points have position vectors `vec(r_(1)) and vec(r_(2))` with respect to origin O.
Take the moment of the forces about the origin the moment of the couple = {sum of the moments of the two forces making the couple}
`vectau=vec(r_(1))xx(-vecF)+vec(r_(2))xxvecF`
`=(vec(r_(2))-vec(r_(1)))xxvecF`
but `vec(r_(1))+vec(AB)=vec(r_(2))`
`therefore vec(AB)=vec(r_(2))-vec(r_(1))`
`therefore` The moment of couple,
`vectau=vec(AB)xxvecF` it means `vec(AB) and vecF` do not depend on origin.
It is independent of the origin, the point about which we took the moment.