Changing part Velocity to shoot in front of the character

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#1

I want to push a part out in a random direction in front of the character within a certain radius, and that radius always stays the same based on what direction the character is facing.

It kind of does it, but the radius changes if the character rotates

local RandomNumber = math.random(-500,500) --Not a set number
local RandomNumber2 = math.random(100,500) --Not a set number
local RandomNumber3 = math.random(100,500) --Not a set number

Part.Velocity = script.Parent.CFrame.LookVector * Vector3.new(RandomNumber,RandomNumber2,RandomNumber3)
#2

I’d work with the cframe rather than the lookVector to adjust, then get the lookVector from that

Velocity = (
   (cframe of script.Parent).Rotation
   * CFrame.Angles(
      0,
      horizontal spread in radians, 
      vertical spread in radians
   )
).LookVector * Speed
#3

Probably a dumb question but to which part exactly does the script belong to?