Final answer:
The forces of 8 N and 12 N can produce a range of resultant forces, with the maximum being 20 N when aligned in the same direction, and the minimum being 4 N when directly opposed. Thus, a resultant force of 4 N cannot occur because it would imply a nonexistent angle of opposition for those magnitudes. Calculations are based on vector addition principles.
Step-by-step explanation:
The question deals with the concept of vector addition in physics. When two forces are applied to a single point, the magnitude of the resultant force depends on both their magnitudes and the angle between their lines of action. According to vector addition, the maximum resultant force occurs when the two forces act along the same line in the same direction, and the minimum resultant force occurs when the two forces act along the same line but in opposite directions.
In this case, the largest possible resultant force that could be produced by two forces of 8 N and 12 N acting in the same direction is 8 N + 12 N = 20 N. Conversely, the smallest possible resultant force, when they act in opposite directions, is 12 N - 8 N = 4 N. Therefore, a resultant force of 20 N is indeed possible, but a resultant force of 4 N cannot be achieved because that would imply the two forces are acting in the opposite direction at an angle that does not exist for these two magnitudes.