Show That If $\mathbf { r } ^ { \prime } ( t )$

Essay

Show that if $\mathbf { r } ^ { \prime } ( t )$ and $\mathbf { r } ^ { \prime \prime } ( t )$ are parallel at some point on the curve described by $\mathbf { r } ( t )$ , then the curvature at that point is 0. Give an example of a curve $\mathbf { r } ( t )$ for which $\mathbf { r } ^ { \prime } ( t )$ and $\mathbf { r } ^ { \prime \prime } ( t )$ are always parallel.