Final answer:
The question addresses the commutative property of addition and multiplication, which states that the sum or product of numbers does not change regardless of the order in which they are combined. This also applies to vector addition, confirming that the resultant vector remains unchanged when the order of vectors being added is altered.
Step-by-step explanation:
Commutative Property of Addition and Multiplication
The question refers to the commutative property of addition and multiplication, which are fundamental principles in mathematics. The commutative property of addition can be expressed as A + B = B + A. This means that the order in which two numbers are added does not change the sum. For example, 2 + 3 yields the same result as 3 + 2, which is 5. Similarly, the commutative property applies to multiplication, expressed as AB = BA. Whether you multiply 2 by 3 or 3 by 2, the product is always 6.
This property is also valid for vectors. When adding vectors, such as A + B + C, reordering them to B + A + C does not affect the resultant vector's magnitude or direction. This demonstrates the commutative property in vector addition, which is crucial in fields such as physics and engineering.
Multiplying or dividing both sides of an equation by the same number does not affect the equation's balance, provided that it is done correctly by distributing the operation across each term in the equation. This is an important aspect when solving for variables within an equation.