Answer
True
Work Step by Step
The statement is true. The vector-valued function describes a line segment: \[ \mathbf{r}(t) = (1 - t)\mathbf{r}_0 + t\mathbf{r}_1, \quad 0 \leq t \leq 1 \]
When \(t = 0\), \(\mathbf{r}(0) = \mathbf{r}_0\), and when \(t = 1\), \(\mathbf{r}(1) = \mathbf{r}_1\). As \(t\) increases from \(0\) to \(1\), \(\mathbf{r}(t)\) changes in a linear fashion to point from \(\mathbf{r}_0\) to \(\mathbf{r}_1\), tracing out a line segment.
Result: True
