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.