Tangent Unit Vector

Topics: Vector

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(definition)

Given $r(t)$ a vector-valued function, we define the tangent unit vector $T(t)$ as:

$$T(t):=\frac{r^{\prime }(t)}{\Vert r^{\prime }(t)\Vert }$$

…given $\Vert r^{\prime }(t)\Vert \ne 0$, of course.

The tangent unit vector helps us define the normal unit vector.