Inner product space

Hi guys I need your help.

We define Inner product space for example of a=(x1,y1,z1) ,b=(x2,y2,z2)like this:

=x1^2+y1^2+z1^2 , =x1x2+y1y2+z1z2

My question is if I need to find this how I will find it?

I will put γ=a+b so γ=(x1+x2,y1+y2,z1+z2) and I will find ? 

And an other question I know norm(a)=IIaII=\(\sqrt{ }\)

Witch is the evidence of Cauchy–Schwarz inequality witch say:

I I ≤ ΙΙαII IIβII 

I don't find the answer in internet I can't underestand it.

Tkank you!