A three dimensional vector \( \vec{r}(t) \) is defined explicitly in terms of the paramater \( t \in \mathbb{R} \), as follows:

\[ \vec{r}(t) = ( x(t), y(t), z(t) ) = (1, 4, 9) + t (1, 2, 3) + t^2 (1, 1, 1) \]

The above vector traces a parabola in 3D. What is the vertex of this parabola ?

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