Couple

Remarks

For every reference point $O$, the total torque of the pair is $(p_1 - O) \times F + (p_2 - O) \times (-F) = M$, so the moment does not depend on $O$. Its size is $\abs{F} d$, where $d$ is the distance between the two lines of action.

Example: $F = (0, 5, 0)$ at $p_1 = (0.2, 0, 0)$ and $-F$ at $p_2 = (-0.2, 0, 0)$ form a couple with moment $(0.4, 0, 0) \times (0, 5, 0) = (0, 0, 2)$.

Non-example: if $p_1 - p_2$ is parallel to $F$, the two forces act along the same line, and their moment is $0$; they cancel completely and do not form a couple. Two couples with the same moment have the same effect on a rigid body, so a couple is often identified with its moment, a free vector.