CHAPTER 3-Subtraction of Vectors

Consider two vectors  and ; we wish to find  such that

We can slightly modify this relation and write it as

and thus subtraction can be treated as addition. To do this, we first reverse the vector  to obtain  and then use the triangle / parallelogram law of addition to add the vector  and :

Joining the tip of  to the tip of  (if  and  are co-initial) also gives us 

Note that from the triangle law, it follows that for three vectors  and representing the sides of a triangle as shown,

We must have

In fact, for the vectors  representing the sides of an -sided polygon as shown,

we must have

since the net effect of all vectors is to bring us back from where we started, and thus our net displacement is the zero vector.