\begin{equation} \textnormal{If } \end{equation} \begin{equation} \textbf{r}(t) = \langle f(t), g(t), h(t) \rangle, \textnormal{then} \end{equation} \begin{equation} \lim_{t \to a} \textbf{r}(t) = \langle \lim_{t \to a} f(t), \lim_{t \to a} g(t), \lim_{t \to a} h(t) \rangle \end{equation} \begin{equation} \textnormal{provided the limits exist.} \end{equation} \begin{equation} \frac{d \textbf{r}}{dt} = \textbf{r}'(t) = \lim_{h \to 0} \frac{\textbf{r}(t + h) - r(t)}{h} \end{equation} \begin{equation} \textnormal{If } \textbf{r}(t) = \langle f(t), g(t), h(t) \rangle = f(t) \, \textbf{i} + g(t) \, \textbf{j} + h(t) \, \textbf{k}, \textnormal{where} f, g, \textnormal{and } h \textnormal{ are differentiable, then } \end{equation} \begin{equation} \textbf{r}'(t) = \langle f'(t), g'(t), h'(t) \rangle = f'(t) \, \textbf{i} + g'(t) \, \textbf{j} + h'(t) \, \textbf{k} \tag{1.1} \end{equation}