Definition:Length (Linear Measure)/Vector

Definition

Let $A$ and $B$ be points in a real Euclidean space $\R^n$.

Let $\mathbf a$ and $\mathbf b$ be the position vectors of $A$ and $B$ respectively.

The length of the straight line $AB$ is given by:

$\map L {AB} := \size {\mathbf a - \mathbf b}$

where:

$\mathbf a - \mathbf b$ denotes the vector subtraction operation

$\size {\mathbf a - \mathbf b}$ denotes the magnitude of $\mathbf a - \mathbf b$.

Also see

• Results about length can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): length
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): length