Definition:Vector Line

Definition
Let $R$ be a region of space in which there exists a vector field $V$ given rise to by a vector quantity $F$.

Let $P$ be an arbitrary point in $V$.

Let the following procedure be established:

Proceed an infinitesimal distance from $P_0$ to $P_1$ in the direction of $\map F {P_0}$.

Proceed an infinitesimal distance from $P_1$ to $P_2$ in the direction of $\map F {P_1}$.

Continue in this manner to trace out a curve in space whose tangent at any point $Q$ gives the direction of the vector quantity $\map F Q$ at $Q$.

This curve is referred to as a vector line.