Hello,

i consider a (smooth) curve in euclidean space $\displaystyle c:I->\mathbb{R}^3$

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$\displaystyle P\in\mathbb{R}^3.$

Then all the tangent lines look like this:

$\displaystyle c(t_0)+t*(P-c(t_0)).$

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

Regards