How to convert Part.Orientation in HumanoidRootPart.CFrame.LookVector and back?

I'm trying to create wall running, and I want the character not to break away from wall during holding a key, if you look to the sides. The idea is that the character's motion vector would coincide with the orientation vector of the wall. Problem is the data types inside Roblox is different and I can't just equate them. (look under comment)

local c = script.Parent
local holdingKey = false
local uis = game:GetService("UserInputService")
local leftAnim = c.Humanoid:LoadAnimation(script:WaitForChild("WallrunLeft"))
local rightAnim = c.Humanoid:LoadAnimation(script:WaitForChild("WallrunRight"))




uis.InputBegan:Connect(function(inp, p)
    if not p and inp.KeyCode == Enum.KeyCode.F then
        holdingKey = true
    end
end)

uis.InputEnded:Connect(function(inp)
    if inp.KeyCode == Enum.KeyCode.F then
        holdingKey = false
    end
end)


game:GetService("RunService").Heartbeat:Connect(function()
    local raycastParams = RaycastParams.new()
    raycastParams.FilterType = Enum.RaycastFilterType.Blacklist; raycastParams.FilterDescendantsInstances = {c}; raycastParams.IgnoreWater = true;
    local rayL = workspace:Raycast(c.HumanoidRootPart.CFrame.Position, -c.HumanoidRootPart.CFrame.RightVector * 3, raycastParams)
    local rayR = workspace:Raycast(c.HumanoidRootPart.CFrame.Position, c.HumanoidRootPart.CFrame.RightVector * 3, raycastParams)
    local ray = rayL or rayR
    if ray and holdingKey then
        if ray == rayL then
            if not leftAnim.IsPlaying then leftAnim:Play() end
            rightAnim:Stop()
        else
            if not rightAnim.IsPlaying then rightAnim:Play() end
            leftAnim:Stop()
        end
        local part = ray.Instance
        local weld = c.HumanoidRootPart:FindFirstChild("WallrunWeld") or Instance.new("WeldConstraint")
        weld.Name = "WallrunWeld"
        weld.Part0 = c.HumanoidRootPart
        weld.Part1 = part
        local bp = c.HumanoidRootPart:FindFirstChild("WallrunBodyPosition") or Instance.new("BodyPosition", c.HumanoidRootPart)
        bp.Name = "WallrunBodyPosition"
        bp.MaxForce = Vector3.new(math.huge, math.huge, math.huge)


        -- implementation of running!!!!!!!
        bp.Position = c.HumanoidRootPart.Position + c.HumanoidRootPart.CFrame.LookVector * (game.Players.LocalPlayer.Character.Humanoid.WalkSpeed*0.5)


        print(ray.Instance.Orientation)
        print(c.HumanoidRootPart.CFrame.LookVector)
    else
        for i, child in pairs(c.HumanoidRootPart:GetChildren()) do
            if child.Name == "WallrunWeld" or child.Name == "WallrunBodyPosition" then
                child:Destroy()
            end
        end
        leftAnim:Stop()
        rightAnim:Stop()
    end
end)