Hello,

i consider a (smooth) curve in euclidean space

and i want to prove:

if all the tangent lines to the curve meet up in a single point, then the curve must be a straight line.

Can you please help me to proove this fact?

Lets say, the point where all the tangent lines meet is

Then all the tangent lines look like this:

But how can i show that c'(t) is constant?

Regards