Definition:Vector Line

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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