Definition:Magnitude

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Definition

The magnitude of a quantity (either vector or scalar) is a measure of how big it is.


It is usually encountered explicitly in the context of vectors:

If $\mathbf v$ is the vector quantity in question, then its magnitude is denoted:

$\size {\mathbf v}$

or

$v$


Also defined as

In Euclidean number theory, the term magnitude is used to mean (strictly) positive real number.


Examples

Arbitrary Example $1$

Let $\mathbf v$ be the position vector in space defined as:

$\mathbf v = x \mathbf i + y \mathbf j + z \mathbf k$

The magnitude of $\mathbf v$ is given by:

$\size {x \mathbf i + y \mathbf j + z \mathbf k} = \sqrt {x^2 + y^2 + z^2}$


Arbitrary Example $2$

Let $\mathbf v$ be the position vector in the plane defined as:

$\mathbf v = x \mathbf i + y \mathbf j$

The magnitude of $\mathbf v$ is given by:

$\size {x \mathbf i + y \mathbf j} = \sqrt {x^2 + y^2}$


Also known as

The magnitude of a vector is also referred to as its module or modulus in some older books.

Some sources refer to it as the absolute value or numerical value of the vector.

The term size can also be seen, generally in popular science books.


Also see

  • Results about magnitude can be found here.


Sources

in which context it is applied to a force only
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