2. Consider the curve \(\vec{r}(t) = (t + 2, 1 - t, \frac{1}{2}t^2)\) for \(t \in \mathbb{R}\).
(i) Calculate the unit tangent \(\vec{T}(t)\), the unit normal \(\vec{N}(t)\), and
the binormal \(\vec{B}(t)\).
(ii) Show that the osculating plane is the same plane for all t.
(iii) What does part (ii) tell you about the curve \(\vec{r}(t)\)?