Vector Function

$\vec{r}(t):\mathbb{R}\to {\mathbb{R}}^n=⟨x_0(t),\cdots ,x_n(t)⟩$ is a vector(-valued) function. $\vec{r}$ is a parameterization A curve $C$ is parameterized by $\vec{r}$ on an interval of $t$

Properties

$$\frac{d}{dt}\vec{r}(t)=\frac{d}{dt}⟨x_0(t),\cdots ,x_n(t)⟩=⟨\frac{d}{dt}{x}_0(t),\cdots ,\frac{d}{dt}{x}_n(t)⟩$$