Explain the commutative law for vector addition.

(N/A) Consider two vectors $\vec{A}$ and $\vec{B}$. According to the parallelogram law of vector addition,we can construct a parallelogram $OPRQ$ where $\vec{OP} = \vec{A}$ and $\vec{OR} = \vec{B}$.
From the triangle law of vector addition in $\Delta OPQ$:
$\vec{A} + \vec{B} = \vec{OP} + \vec{PQ} = \vec{OQ} \quad \dots (i)$
From the triangle law of vector addition in $\Delta ORQ$:
$\vec{B} + \vec{A} = \vec{OR} + \vec{RQ} = \vec{OQ} \quad \dots (ii)$
Since $\vec{PQ} = \vec{OR} = \vec{B}$ and $\vec{RQ} = \vec{OP} = \vec{A}$ in a parallelogram,comparing equations $(i)$ and $(ii)$,we get:
$\vec{A} + \vec{B} = \vec{B} + \vec{A}$
This proves that vector addition is commutative.