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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 $0$?

2 Answers 2