Which one of the following vectors in $\mathbb{R}^3$ is a unit vector that is parallel to the plane with general equation $2x+2y+z=1$?
$a) (2/3, -1/3, -2/3) $ $b) (-3, 2, 2)$ $c) (2/3, 2/3, -1/3)$ $d) (1/2, 1/2, 1/\sqrt{2})$
Would I be correct in choosing a) as the magnitude of the vector is $1$ and the dot product of $(2/3, -1/3, -2/3)$ and the normal vector to the plane is $0$?