Where am I confused about force addition?

Question

As far as my knowledge is concerned, a vector quantity should possess magnitude and direction & more over it should also obey the laws of vector addition. As we all know that the vector sum of 3 newtons in the x direction and 4 newtons in the y direction will acting at a point will produce a resultant of 5 newtons. Where did the remaining 2 newtons go? I mean we have applied a total of 7 newtons of force on a point sized particle but the output is only 5 newtons, so it appears as if a 2 newton force is disappearing here. In which other form does it reappear rather than the resultant? Or is it something like the remaining 2 newtons of force just vanishes and it doesn't appears in any other form? Please correct me if I am going wrong on this issue.

Answer 1

The best answer to this, I think, is to consider an analogy with displacement. Suppose you walk three meters east, then turn and walk four meters north. You walked seven meters. But your displacement is only five meters from the starting point. Where did those other two meters "go"? Well, nowhere, in a manner of speaking. You just walked seven meters in distance to achieve a displacement of five meters. The other two meters did not "vanish." They were just additional distance when the walking was done in this configuration. This illustrates the difference between arithmetic addition (which has no way to account for direction in two or more dimensions) and vector addition (which does).

In the same way, with the forces, a total magnitude of 7 N of force was used to achieve a *net* force of 5 N, based on the two-dimensional configuration.