Final Answer:
The vector sum of momenta in a collision remains constant.
Step-by-step explanation
During a collision between objects, the total momentum of the system before the collision equals the total momentum after the collision. This principle is derived from the law of conservation of momentum, which states that in an isolated system, the total momentum remains constant if no external forces act upon it.
This means that the vector sum of the momenta of all objects involved in a collision (considered as a closed system) remains unchanged both before and after the collision.
In any collision, be it elastic or inelastic, the sum of the momenta in all directions (x, y, z) remains constant. Even if individual objects may experience changes in momentum due to internal forces, the overall total momentum of the system remains constant over time. This principle is fundamental in understanding and predicting the outcomes of collisions in physics.