Explain the Properties Of Vector Addition?

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Properties Of Vector Addition
For any 2 vectors a and b
a plus b is equal to b plus a
Consider a parallelogram ABCD Let AB be equal to a and BC be equal to b.
Using triangle Law in triangle ABC we get AC is equal to a plus b since the opposite side of a parallelogram are equal and parallel. We get AD is equal to BC is equal to b and Dc is equal to AB is equal to a.
Again using triangle Law in triangle ABC we get AC is equal to b plus a Hence a plus b is equal to b plus a.
This is the commutative property of vector addition.
for any 3 vectors a, b and c
a plus b plus c is equal to a plus b plus c. let the vectors a ,b and c be represented by PQ, QR and RS respectively.
Using triangle Law in triangle PQR we get a plus b is equal to PQ plus QR is equal to PR
Using triangle Law in triangle PRS we get a plus b plus c is equal to PR plus RS is equal to PS
Using triangle Law in triangle QRS we get b plus c is equal to QR plus RS is equal to QS
Using triangle Law in triangle PQS we get a plus b plus c is equal to PQ plus QS equal to PS
Hence, a plus b plus c is equal to a plus b plus c.
This is the Associative property of vector addition.