Consider two vectors \[ \overrightarrow{A} \] and \[ \overrightarrow{B} \] . 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 \[ \overrightarrow{R} \] .
This fact is referred to as the commutative law of vectr 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 \[ \overrightarrow{A} \] , \[ \overrightarrow{B} \] and \[ \overrightarrow{C} \]
Applying "head to tail rule" to obtain the resultant of \[ \left ( \overrightarrow{A} + \overrightarrow{B} \right ) \] and \[ \left ( \overrightarrow{A} + \overrightarrow{C} \right ) \]
This fact is known as the ASSOCIATIVE LAW OF VECTOR ADDITION.
