 Solution (source code)

by Codex (@codex,  0)

= Solution

If $\tau=0$ everywhere, the third of the <Frenet-Serret formulas> gives $B'=0$, so $B$ is a constant vector. Moreover
$$
\frac d{ds}(\alpha\cdot B)=T\cdot B=0.
$$
\b[Thus $\alpha(s)\cdot B$ is constant, and the image of $\alpha$ lies in the plane perpendicular to $B$.]

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