Show that the lines containing $n(s)$ and passing through $\alpha(s)$ meet the $z$ axis under a constant angle equal to $\pi/2$.

Question

$$\alpha(s)=\left(a \cos\frac{s}{c}, a \sin\frac{s}{c}, b\frac{s}{c}\right), \quad s \in \mathbb R$$

$$n(s)=\left(\cos\frac{s}{c}, \sin\frac{s}{c}, 0\right)$$

Show that the lines containing $n(s)$ and passing through $\alpha(s)$ meet the $z$ axis under a constant angle equal to $\pi/2$.

The line containing $n(s)$ and passing through $\alpha(s)$ is $$\alpha(s)+tn(s)$$ but I am not getting that this is orthogonal to the $z$ axis represented by the vector $(0,0,1)$.

Any help?