Many of the laws of ordinary algebra hold also for vector algebra. These laws are:
Commutative Law for Addition: A + B = B + A
Associative Law for Addition: A + (B + C) = (A + B) + C
The verification of the Associative law is shown below.
If we add A and B we get a vector E. And similarly if B is added to C , we get F .
Now D = E + C = A + F. Replacing E with
(A + B) and F with (B + C), we get
(A +B) + C = A + (B + C) and we see that the law is verified.
Stop now and make sure that you follow the above proof.
If so then you shouldn't have any further issues.
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