# Math Help - Mutually perpendicular vectors

1. ## Mutually perpendicular vectors

"Verify that if a and b are vectors of the same length then
a + b and a - 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?

2. $(a+b)\cdot{(a-b)}= a\cdot a+b\cdot a-a\cdot b-b\cdot b$

Now use

$x\cdot x= \left\|{x}\right\|^2$ .