Find all unit vectors parallel to the xy-plane and perpendicular to the vector [1, -2, 2].

so

$\displaystyle

a=[1,-2,2]$

$\displaystyle v=[x,y,0]$

Using Dot Product

$\displaystyle adotb=0$

$\displaystyle 1x-2y+2(0)=0$

After that i rearrange and get stuck with x-x=0... I don't see any other ways to do this.