If $\alpha(s)$ is a planar curve $\iff \tau = 0, \tau $ is torsion.
Can you tell me is my proof correct?
Let normal to plane be $ \vec V$. As it is planar curve $\vec V = \vec c$, a constant vector
We know that Tangent $\vec T$ and normal $\vec N$ to $\alpha(s)$ are normal to each other and also perpendicular to $\vec V$
Binormal $\vec B = \vec T \times \vec N = b\vec V$, where b is constant
$\frac{d \vec B}{ds} = b \frac{d\vec V}{dx} = \vec 0$ as $\vec V $ is constant vector
i.e., $\tau = 0$
Is this proof correct? in text book i see a much more detailed proof...Pls correct me if i am going wrong