Answer
False
Work Step by Step
The statement is false. A vector-valued function that has two component functions such as \[ \mathbf{r}(t) = \langle x(t), y(t) \rangle \] describes a curve in 2-space. For each value of \(t\) in its domain, \(\mathbf{r}(t)\) is a vector from the origin pointing to a specific point on the curve. If it had three component functions, \[ \mathbf{r}(t) = \langle x(t), y(t), z(t) \rangle \] it would still describe a curve, but in 3-space.
Result: False
