Orthogonality of Absolute Derivative

[rbwang1225]

Hello!
Is any covariant vector orthogonal to absolute derivative of its contravariant counterpart?
I read a GR book, and it says the tangent vector of a curve is orthogonal to its absolute derivative, that is $D\lambda^A/dst_A=0$, where $t^A$ is the unit tangent vector of some curve $\gamma$.

Any comments would be appreciated.

 

[rbwang1225]

Oh! I am very sorry. It's very straight forward. Since $t^At_A=1, Dt^A/dst_A=0$