COMMUTATIVE LAW AND ASSOCIATIVE LAW OF VECTOR ADDITION



PROPERTIES OF VECTOR ADDITION
COMMUTATIVE LAW
OF
VECTOR ADDITION
Consider two vectors and  . Let these two vectors represent two adjacent sides of a parallelogram. We construct a parallelogram
OACB as shown in the diagram. The diagonal OC represents the resultant vector 
COMMUTATIVE LAW OF VECTOR ADDITION
From above figure it is clear that:
This fact is referred to as the commutative law of vectr addition .
ASSOCIATIVE LAW
OF
VECTOR ADDITION
The law states that the sum of vectors remains same irrespective of their order or grouping in which they are arranged.
Consider three vectors  and 
Applying “head to tail rule” to obtain the resultant of () and ()
Then finally again find the resultant of these three vectors :
ASSOCIATIVE LAW OF VECTOR ADDITION
This fact is known as the ASSOCIATIVE LAW OF VECTOR ADDITION.

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