Chapter 12 - Vector-Valued Functions - 12.6 Motion Along A Curve - Exercises Set 12.6 - Page 893: 49

False

Let \[ \mathbf{r}(t) = (\ln t)\mathbf{i} + (\sin(\ln t))\mathbf{j}. \] Then \[ \kappa(1) = 0, \quad \mathbf{v}(1) = \mathbf{i} + \mathbf{j}, \quad \text{and} \quad \mathbf{a}(1) = -\mathbf{i} - \mathbf{j}. \] \[ \mathbf{a} \text{ and } \mathbf{v} \text{ are parallel, but they are in opposite directions.} \] Result: False