Normal component

A vector in three-dimensional space can be clearly broken down into a parallel component and a normal component in relation to a direction or a plane : ${\displaystyle \mathbb {R} ^{3}}$ ${\displaystyle {\vec {a}}_{\perp }}$

${\displaystyle {\vec {a}}={\vec {a}}_{\parallel }+{\vec {a}}_{\perp }}$

In it is

${\displaystyle {\vec {a}}}$: any vector in the ${\displaystyle \mathbb {R} ^{3}}$

${\displaystyle {\vec {a}}_{\parallel }}$: a vector parallel to the selected direction or plane

${\displaystyle {\vec {a}}_{\perp }}$: a vector perpendicular to the selected direction or plane.

The decomposition does not require that a specific coordinate system is defined.

See also

• Normal vector
• Direction vector