Suppose all the tangent lines of a space curve pass through a fixed point. What can we say about the curve?
Proof starts like this in the textbook
Without loss of generality, we take the fixed point to be the origin and the curve to be arc length-parametrized by $\vec α$. Then for every s we have $\vec α(s) = λ(s)\vec T(s)$ for some scalar function $λ.$ I have a doubt here. What guarentees the existance of scalar function $λ?$
My attempt:- I know the $\vec α'(s)$ indicate the direction of tangent vector to the curve $\vec α(s)$. $\vec α'(s)=\vec{T}(s).$ I couldn't find the scope of $\lambda$. Could you help me?