The addition of two vectors and is done by adding in corresponding components of both vectors. For two, three and -dimensions, the addition looks like this:

(1)

This can be represented graphically as follows:

The resulting vector (green) of the addition is found by moving the vector to the head of vector or vice versa.

**Example**

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

(2)

**Rules**

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