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.
Also known as
A vector line is also known as:
- a line of flow
- a flux line
- a field line.
In contexts where the vector field in question is (or gives rise to) a force, then the term line of force can be seen.
Examples
Line of Electric Force
A line of (electric) force is a vector line of an electric field.
Also see
- Results about vector lines can be found here.
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $5$. Scalar and Vector Fields