The resultant couple moment is a vector quantity. In order to understand why, let's first define what a couple is and what a moment is.

- Couple: A couple is a system of forces that consists of two equal and opposite forces acting on a body, but not along the same line of action. These forces create a moment or torque.

- Moment: Moment is the turning effect of a force about a point or an axis. It is a vector quantity that is defined by the magnitude, direction, and the line of action of the force.

Now, let's discuss why the resultant couple moment is a vector quantity:

1. Vector Addition:
When multiple couples act on a body, the resultant couple moment is obtained by vector addition of the individual couple moments. Vector addition follows the rules of vector algebra, where both magnitude and direction are considered. Therefore, the resultant couple moment is a vector quantity.

2. Magnitude and Direction:
The magnitude of a couple moment is given by the product of one of the forces and the perpendicular distance between the forces. The direction of the couple moment is perpendicular to the plane formed by the two forces and follows the right-hand rule. Since both magnitude and direction are taken into account, the resultant couple moment is a vector quantity.

3. Line of Action:
The line of action of a couple moment is the axis about which the body tends to rotate. The line of action is defined by the direction of the couple moment vector. Different couples can have different lines of action, which can be parallel or intersecting. Therefore, the resultant couple moment, obtained by vector addition, will have its own unique line of action, making it a vector quantity.

Conclusion:
In conclusion, the resultant couple moment is a vector quantity because it follows the rules of vector addition, takes into account both magnitude and direction, and has its own unique line of action. It is important to understand the vector nature of the resultant couple moment in order to accurately analyze the equilibrium or motion of a body under the influence of multiple couples.