Calculus: Early Transcendentals 8th Edition

Suppose $R(t)$ is a position vector of a space curve $C$ at a point $A$. Thus, the tangent vector is defined as $R'(t)$.The tangent line at point $A$ is said to be the line passing through the point $A$ which is further parallel to the tangent vector, that is, $R'(t)$. Now, the unit tangent vector let us say $T(t)$ is defined as: $$T(t)=\dfrac{R'(t)}{|R'(t)|}$$