Show that there is a fixed $p \in \mathbb{R}^n$ such that for all $s \in I, \gamma(s)=\beta(s)+p$.

Question

Suppose that $\beta,\gamma : I \to \mathbb R^3$ are two unit speed smooth curves. Suppose that the curvatures and tortions are everywhere positive, and that $B_\beta(s)= B_\gamma(s)$ for all $s\in I$. Show that there is a fixed $p \in \mathbb R^3$ such that $\gamma(s)= \beta(s)+p$ ,for all $s \in I,.$