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

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 :

This fact is known as the ASSOCIATIVE LAW OF VECTOR ADDITION.

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