Again I have a question, it's about a proof, if the torsion of a curve is zero, we have that
$$ B(s) = v_0,$$
a constant vector (where $B$ is the binormal), the proof ends concluding that the curve $$ \alpha \left( t \right) $$ is such that $$ \alpha(t)\cdot v_0 = k $$ and then the book says, "then the curve is contained in a plane orthogonal to $v_0$." It's a not so important detail but .... that angle might not be $0$, could be not perpendicular to it, anyway, geometrically I see it that $ V_0 $ "cuts" that plane with some angle.
My stupid question is why this constant $k$ must be $0$. Or just I can choose some $v_0 $ to get that "$k$"?