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Addition of Vectors


Consider the coplanar vectors A, o and C as shown in Fig. 2.1. We represent the different  resultants by dotted lines. A is added to B by law of parallelogram, and we get resultant  as (A+ B). Now again we apply parallelogram law for vectors (A+ B) and C. Thus, we get the resultant vector (:A ,..B) + C (Refer Fig. 2.l(a)

Let us now add B with c and then A we get the resultant as (8 +c)+ A. (Refer Fig. 2.1(b))


We notice that the final vector is identical for both procedures. So,

This is the associative law of vectors. The addition of vectors is also cumulative.