Question

What is the definition of vector addition?

Answer 1

Vectors can be added by adding the components individually as long as they have the same dimensions. Adding two vectors simply gives you a resultant vector.

What that resultant vector means depends on what quantity the vector represents. If you are adding a velocity with a change of velocity, then you would get your new velocity. If you are adding 2 forces, then you would get a net force.

If you are adding two vectors that have the same magnitude but opposite directions, your resultant vector would be zero. If you are adding two vectors that are in the same direction, then the result is in the same direction with a magnitude that is the sum of the 2 magnitudes.