How to find vector coords in some other coord system ?

Unity Engine
1

Lets say we have a normal coord system, and a vector defined in it as v(-0.5, 0, -1). And that there is another coord system (of an object) located at (2, 1, 1) and it is rotated by facing directly on opposite z, that is its x and y are the same as original coord system but its z is pointing in (0, 0, -1) in respect to original coord system.

What I want to know what are the coords of vector v in respect to the second coord system.

2

Probably otherTransform.TransformPoint(v3)

3

I have found the solution. There just needs to be computed the inverse of that rotation.
So using quaternions its Quaternion.Inverse().