How would I keep a part at a certain distance from the player's head at all times?

I'm making a script that allows you to pick up certain parts by pressing 'E'. The object will then hover in front of the player's head (locked to their mouse as I tried to use the head and couldn't figure it out), and the player then can choose to drop it by pressing E again, like in Half-Life or Portal. But, I've hit a roadblock. The object will keep flying into the camera, and if the player points at the sky (for example), the object will go too far out. Basically, how can I lock it at a certain distance but maintain it's ability to follow the mouse? (Background info: Player will be in First Person)

local object
local Player = game.Players.LocalPlayer
local Character = Player.Character
local PlrMouse = Player:GetMouse()
local Camera = game.Workspace.CurrentCamera

while true do
	wait()
	while script.Parent.Grabbing.Value == true do
		object = script.Parent.Obj.Value
		object.CanCollide = false
		wait()
		rot = Vector3.new(PlrMouse.Hit.X, PlrMouse.Hit.Y, PlrMouse.Hit.Z)
		object.Position = rot
	end
end

local object
local Player = game.Players.LocalPlayer
local Character = Player.Character
local PlrMouse = Player:GetMouse()
local Camera = game.Workspace.CurrentCamera

while true do
    wait()
    while script.Parent.Grabbing.Value == true do
        object = script.Parent.Obj.Value
        object.CanCollide = false
        wait()
        rot = Vector3.new(PlrMouse.X, PlrMouse.Y, PlrMouse.Z)
        object.Position = rot
    end
end

--Try origin not hit. Tell me if it works.-- Try the new code