How to handle this curve?

Question

I started with differentiation of all three coordinates of this parametrically given curve.

I want to show that the respective curve has related equation of the plane and also to prove that it a "plane-curve".

$$\gamma\left(t\right)=\left(\frac{1+t^2}t\;,\;{t+1}\;,\;\frac{1-t}t\right)$$

Answer 1

Hint: Show that torsion is null. You can see the formules here.

Answer 2

Note that $x(t)-z(t)=y(t)$, which implies that the curve lies in the plane $x-y-z=0$.