Vector addition is commutative, which means that the order in which vectors are added does not affect the result. In other words, if we have two vectors A and B, the addition of A and B will be the same regardless of whether we add A to B or B to A.

Explanation:
Commutative property of addition states that for any two vectors A and B, A + B = B + A.

Proof:
To prove that vector addition is commutative, let's consider two vectors A and B in a two-dimensional space.

A = (A1, A2)
B = (B1, B2)

When we add A to B, we get a new vector C:

C = A + B = (A1 + B1, A2 + B2)

Now, let's add B to A:

D = B + A = (B1 + A1, B2 + A2)

Comparing C and D, we can see that they are equal:

C = D = (A1 + B1, A2 + B2) = (B1 + A1, B2 + A2)

Thus, we have shown that A + B = B + A, which proves the commutative property of vector addition.

Visual representation:
To further illustrate this concept, consider a graph with two vectors A and B. When we add A to B, we can visualize it by placing the tail of A at the head of B and drawing a new vector from the tail of B to the head of A. The resulting vector will be the same if we add B to A, as shown in the diagram below:

------> B
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|
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A ------>

------> A
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B ------>

Conclusion:
Vector addition is commutative, meaning that the order in which vectors are added does not affect the result. This property is fundamental in many applications of vector algebra, allowing us to freely rearrange vectors in equations and calculations without changing the outcome.