Given
$$\alpha(t)=\left(t,\frac{1+t}{t},\frac{1-t^2}{t}\right)$$
I want to know if there is way of knowing if this curve is plane or not without calculating its torsion.
I considered the option of trying to know if its contained in a plane. But I don't know how to proceed. Any ideas? Thanks in advance.
Best Answer
${{1+t}\over t}-{{1-t^2}\over t}-t=1$ so the curve is in the plane $-x+y-z=1$