Hi MHF

This is my first post, I'm faaaairly certain this is in the right subforum, sorry if it isn't.

Anyway, I'm having difficulty with vector algebra, more specifically, proving one expression equals another

I have this question:

"Prove (a-b) x (a+b) = 2(axb)"

Whereaandbare both vectors and x= cross product

The problem is, I am getting confused over what rules I can use from traditional algebra (ie taking a and b as just variables) and the vector specific rules, (ie commutative laws, distributive laws, etc)

I have another one too:

" if (c-0.5a).a= (c-0.5b).b= 0 then, provec-0.5(a+b) is perpendicular toa - b"

where . = dot product

(Sorry if that one is confusing, typing out 1/2 was a bit messy compared to just typing 0.5)

I know that vectors are perpendicular if they have a dot product of 0, but (again) I'm just quite confused about what rules I can use here.

Thanks very much