Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 815: 21

$\textbf{T}(t) = \langle \frac{2}{3}, \frac{2}{3}, \frac{1}{3}\rangle$

$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$ $\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$ $\textbf{r}(t) = \langle 2t,2t,t\rangle$ $\textbf{r}'(t) = \langle 2,2,1\rangle$ $|\textbf{r}'(t)| = \sqrt {(2)^2 + (2)^2 + (1)^2} = \sqrt {9} = 3$ $\textbf{T}(t) = \frac{\textbf{r}'(t)}{|\textbf{r}'(t)|} = \frac{\langle 2,2,1\rangle}{3} = \langle \frac{2}{3}, \frac{2}{3}, \frac{1}{3}\rangle$