Extremely confused. "show that the two vectors can be added as a + b or as b + a yet still provide the same resultant.

You can prove this by using the commutative property:

a + b = b + a

basically, as long as they are the same length

a + b = c(resultant vector) 

and

b + a = c(resultant vector.

hope this helps

The modern-day generator works on the principle of electromagnetic induction discovered by michael faraday in 1831-32. faraday discovered that the above flow of electric charges could be induced by moving an electrical conductor, such as a wire that contains electric charges, in a magnetic field.