# Parametric Parabola in 3D Space

Geometry Level pending

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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