Consider the helix $r(t) =\langle \cos t,\, \sin t,\, t\rangle$, for $\:- \infty < t < \infty$. Find all points on the helix at which $r$ and $r'$ are orthogonal.
What steps do you take in finding the points on the helix at which $r$ and $r'$ are orthogonal?
First, you need to ask yourself what it orthogonality means. Also, we need to compute $r_t$ \begin{equation} r_t = (-\sin{t}, \cos{t}, 1) \end{equation} Do you know when two vectors are orthogonal? If not, it means that the inner product $\langle r_t, r \rangle$ is equal to $0$. Or \begin{equation} \langle r_t, r \rangle = -\sin{t}\cos{t} + \sin{t}\cos{t} + t = 0 \end{equation} Which you will need to solve, which should be easy! Then, I think you should be able to finish the exercise now :)