Prove for generic vectors i, 3, w in R3 and c, d in R the algebraic properties of vectors. [Hint: each vector property can be reduced to properties of real numbers and definitions. These should all be...

Please include properties and rules for each step

I need explains for each step

Extracted text: Prove for generic vectors i, 3, w in R3 and c, d in R the algebraic properties of vectors. [Hint: each vector property can be reduced to properties of real numbers and definitions. These should all be relatively short. Some will be very short.] a. + ở = ở + ủ b. (u + ở) + w = ủ + (ở + w)