Translate a set of points

This is most likely a basic question but i cannot seem to find the correct answer.
I have a set of points that i want to alter based on the following:
A 3d vector is defined, say (300,0,500). This vector is supposed to be my new X axis. What formula must be applied to each point to make this change, and how do i do that in Unity?

Cheers

EDIT: Let me give some more insight: I have a set of points that comprise a larger one, a “point cloud” if you would like. This cloud rotates, moves in the scene e.t.c. However, at certain time intervals I have the aforementioned vector, which starts from the cloud’s left most point and ends at the right most point ( in the case where the object rotated, it’s the inverse). I want to have a separate area in my scene where I translate all of the points comprising the object to a view that does not change with rotation or translation of the original object, so as to view the object’s front if you like (again, this will happen only at the time intervals the vector is available).
Hopefully it’s more clear now.

i think it is something like this

GameObject array = new GameObject[#objects];

		for(int i=0;if<array.Length;if++){
			Array *= GameObject("object");*
  •  }*
    
  •  Vector3 Test = new Vector3(300,0,500);*
    
  •  for(int i=0;if<array.Length;if++){*
    

_ Array*.transform.position = Test.x;_
_
}*_