Question

State and prove (draw vector diagram) commutative law of vectors,​

Answer 1

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.