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

(1)   equation

This can be represented graphically as follows:


The resulting vector (green) of the subtraction is going from the head of vector equation to the head of vector equation. This is the same as adding the vector equation (flipping the orientation of equation) to equation 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.


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

(2)   equation


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