"Verify that ifaandbare vectors of the same length then

a+banda-b

are mutually perpendicular."

How are you able to figure out how to verify that the vectors are the same length/mutually perpendicular? I know that you use the dot product, so (B]a[/B] +b) · (a-b) to verify it although, I just do not understand why. How does the dot product of both vectors mean that they are of the same length/mutually perpendicular?