The subtraction of two vectors and is done by subtracting the corresponding components of both vectors, similarly to addition of vectors. For two, three and -dimensions, the subtraction looks like this:

(1)

This can be represented graphically as follows:

The resulting vector (green) of the subtraction is going from the head of vector to the head of vector . This is the same as adding the vector (flipping the orientation of ) to as can be seen in the diagram as the addition of the blue and purple vectors. The resulting green vector is the identical to the one obtained from the subtraction.

**Example**

Consider the following vectors three-dimensional and and we show how they are subtracted to make a new vector :

(2)

**Rules**

Vector subtraction, like normal subtraction is associative (the brackets can be changed arround: ) and it is *not* commutative (the order *does matter*: ).