Local offset in right

I want the HUD to always be to the right of the character. But when I use vector3 it shifts depending on which way the character is looking. That is, it can move forward, backward, left, right relative to the world axis

HUDClone.CFrame = character.HumanoidRootPart.CFrame + character.HumanoidRootPart.CFrame.LookVector + Vector3.new(3,0,0)

Character spawned facing X axis

Character spawned facing Y axis

If you want it to be on the right, use RightVector instead

local HRP = CHARACTER:WaitForChild('HumanoidRootPart')
HUD.CFrame =  CFrame.new(HRP.Position + (HRP.CFrame.RightVector * 3))
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You probably just mean to do

HUDClone.CFrame = character.HumanoidRootPart.CFrame * CFrame.new(3, 0, 0)
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Thanks everyone for the help! both codes helped me!