Final answer:
The property where A + B equals B + A, regardless of the order of addition, is known as the Commutative Property. This applies to both numbers and vector addition, demonstrating that sum remains unchanged with order.
Step-by-step explanation:
The property described in the question, where A + B = B + A, is known as the Commutative Property of addition. This property states that the order in which two numbers are added does not change the sum. This is a fundamental property of addition in mathematics that is also applicable in the addition of vectors, where vector A plus vector B is the same as vector B plus vector A, and the resultant sum vector remains unchanged regardless of the order of addition.
To further exemplify this property with vector addition, when adding three vectors A, B, and C with different lengths and directions, the order in which they are added does not affect the sum. For instance, A + B + C will have the same sum as B + C + A or any other order in which these three vectors might be combined.