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Prove that parallel translation has the following properties:

• [math]|T_{P_0} (\vec u)| = |\vec u|[/math] for every vector [math]\vec u[/math].
• If [math]\vec u[/math] is any vector in [math]V_{P_0}[/math], then [math]T_{P_0}(\vec u) = \vec u[/math].
• If [math]\vec 0[/math] is any zero vector, then [math]T_{P_0}(\vec 0)[/math] is also a zero vector.