Final answer:
The most precise determination of the correct relationship between the net force and the vector sum of the individual forces exerted on the cart can be obtained by analyzing the measurements of the force Fo and the tension Fr.
Step-by-step explanation:
The most precise determination of the correct relationship between the net force and the vector sum of the individual forces exerted on the cart can be obtained by analyzing the measurements of the force Fo (force to hold the cart in place) and the tension Fr (horizontal tension of the string).
In this case, the set of measurements that would provide the most precise determination is option c. with Fo: 20 N, 19 N, 18 N and Fr: 50 N, 49 N, 48 N.