(B) SUBTRACTION OF VECTORS : An extension of addition
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 (- ):
(i) Reverse to obtain –
(ii) Add and (-) to obtain –
OR
(i) Make and co-initial.
(ii) Join the tip of to the tip of to obtain –
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 atriangle as shown,
we must have + + = 
In fact, for the vectors , ,i = 1,2, ….n , a representing the sides of an n-sided polygon as shown,
we must have
1 + 2 + …….+ n =
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.
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