Final answer:
The subject is based on the commutative property of addition, as it relates to vector and scalar addition. It demonstrates how the order of adding integers or vectors, a + b or b + a, does not affect the final sum or resultant vector.
Step-by-step explanation:
The question relates to the properties of integer addition and the order of operation, specifically within the context of vector addition. In mathematics, the commutative property states that the order in which two numbers are added does not affect the sum, which is expressed as A + B = B + A. This applies to both scalars and vectors. Indeed, for vectors, adding vector a to vector b yields the same resultant vector as adding vector b to vector a. This is shown in the equation a + b = b + a, which is true regardless of the dimensions in which these vectors exist.
Several common rules of addition can be exemplified by this principle. For instance, when two positive numbers are added together, the result is positive, as in 3 + 2 = 5. Conversely, when two negative numbers are added, the result is negative, as in -4 + (-2) = -6. When adding numbers with opposite signs, the smaller number is subtracted from the larger number, with the resultant sum having the sign of the larger number; for example, -5 + 3 = -2. When subtracting, one can change the sign of the subtracted number and then apply the rules of addition.