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

(1)   equation

This can be represented graphically as follows:


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


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

(2)   equation


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