What is the geodesic of the helicoid?
$M=\{ (x,y,z)\in \mathbb{R}^3: x\sin z - y\cos z =0\}$
Whose tangent at the point $p = (1,0,0)$ in the line $r = \{(x, y, z) \in \mathbb {R} ^ 3: x = 1, y = z\}$.
I tried with the definition, but I don't know the parameterization, and so do not know which is the tangent plane. I can't do $\alpha ''(t) \perp T_{\alpha(t)}M$.
Any help is appreciated.