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 threedimensional Euclidean space R^{3} the amount of a vector is calculated according to the following formula, where a_{x}, a_{y} and a_{z }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 
Example:
The amount of  is 
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