**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 vector 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:

Applying “head to tail rule” to obtain the resultant of:

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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