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

question 35

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.

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Definitions:

Lone Pair Electrons

A pair of valence electrons that are not shared with another atom and hence do not participate in bonding but influence molecular shape and polarity.

Hydrogen Chloride

A diatomic molecule composed of hydrogen and chlorine; when dissolved in water, it forms hydrochloric acid.

Lewis Structure

A representation of molecules showing how the valence electrons are arranged among atoms in the molecule.

Ethane

A colorless, odorless gas that is the second simplest alkane, consisting of two carbon atoms and six hydrogen atoms.