Earlier in this lesson we introduced a new vector, the unit tangent [math]\vec{T}\left(t\right)=\frac{\vec{c}'\left(t\right)}{\left|\left|\vec{c}'\left(t\right)\right|\right|}[/math], which has given us information about the image curve of a path. There is a second useful vector called the [b][color=#ff0000]unit normal vector[/color][/b], defined as follows:[br][br][math]\vec{N}\left(t\right)=\frac{\vec{T}'\left(t\right)}{\left|\left|\vec{T}'\left(t\right)\right|\right|}[/math][br][br]In other words, the unit normal vector to a path [math]\vec{c}\left(t\right)[/math] is the unit tangent to the unit tangent to [math]\vec{c}[/math].[br][br]Experiment with the applet below. Make some observations about the behavior of the unit normal vector.