Explain why vector addition is not commutative.

Vector addition is commutative because the order in which vectors are added does not change the resultant vector.

In more detail, the commutative property refers to the ability to swap the order of operations without changing the outcome. For example, in arithmetic, the numbers 2 and 3 can be added together in any order (2+3 or 3+2) and the result will always be 5. This is because addition of numbers is commutative.

However, when it comes to vectors, the situation is different. Vectors are quantities that have both magnitude (size) and direction. When you add vectors, you're combining both these aspects. The key point is that the order in which you add vectors does not change the final result. This is because the resultant vector is simply the sum of the individual vectors, regardless of the order in which they were added.

For example, consider two vectors A and B. If you first add A to B, you'll get a resultant vector R. If you then add B to A, you'll get the same resultant vector R. This is because the process of vector addition involves placing the tail of the second vector at the head of the first vector, and then drawing a new vector from the tail of the first vector to the head of the second vector. This process is the same regardless of the order in which the vectors are added.

Therefore, vector addition is commutative because the order in which vectors are added does not change the resultant vector. This is a fundamental property of vectors and is crucial for solving problems in physics where vectors are involved.