The Plane $x + 2 y + z = 0$ Has a Normal

Essay

The plane $x + 2 y + z = 0$ has a normal $\vec { n } = \vec { i } + 2 \vec { j } + \vec { k }$ Let $\vec { u } = \vec { i } + \vec { j } + \vec { k }$ .Express $\vec { u }$ as the sum of a vector $\vec { v }$ which is parallel to $\vec { n }$ and a vector $\vec { w }$ which is parallel to the plane.