Has a zero vector one unit

The length (the amount) of a vector Andreas Pester University of Applied Sciences Techikum Kärnten, Villach
[email protected]Summary: In this section the term length (amount) of a vector is explained

Keywords: Definition | Normalized vector | Properties of the amount

The Length of a vector is in math Amount of the vector called.

Length (amount) of the vector :


The magnitude of a vector is a scalar quantity and is always positive, unless it is a zero vector (amount equal to zero). The zero vector has length zero and any direction.

For the three-dimensional Euclidean space R3 the amount of a vector is calculated according to the following formula, where ax, ay and az the vector coordinates are:


The sign T just means that the vector is transposed. This operation turns a row vector into a column vector, and vice versa, a column vector becomes a row vector.

A vector is called normalized, if

applies. It has the length 1.

If holds, we can use the vector normalize according to the following formula:

is the normalized vector
It applies


The amount of is