Given a nonzero vector \(\Vect{a}\) in \(\RNrSpc{n}\), the hyperspace perpendicular to \(\Vect{a}\) is the set

\[\OrthCmplmntOf{\Vect{a}}\DefEq \text{Perp}(\Vect{a}) \DefEq \Set{ \Vect{x} \in \RNrSpc{n} \st \DotPr{\Vect{a}}{\Vect{x}} = 0}\]

The vector \(\Vect{a}\) is called a normal vector of \(\text{Perp}(\Vect{a})\).