Derivative of normal vector field of $k$-submanifold

Question

Let $\Sigma$ be a $k$ submanifold in $n$-Riemannian manifold $N$, suppose we have normal vector fields $\nu_1,\cdots,\nu_{n-k}$ and they are O.N. basis of normal space. Let $X\in \Gamma(T\Sigma)$, I want to calculate $\nabla_{X}\nu_1$ here $\nabla$ is the Levi-Civita connection in $N$. I know that $\nabla_X\nu_1$ doesn't have component in $\nu_1$ direction since $\langle \nabla_X\nu_1,\nu_1\rangle=\frac{1}{2}\nabla_X|\nu_1|^2=0$. I am wondering if it has component in other normal directions, all I know so far is $\langle \nabla_X\nu_1,\nu_i\rangle=-\langle \nabla_X\nu_i,\nu_1\rangle$. In fact, all I want to know is if it is tangent to $\Sigma$ ?