The datum of an inner product entails that lengths of vectors can be defined too, by defining the associated norm | v | := ⟨ v , v ⟩ {\displaystyle |\mathbf {v} |:={\sqrt {\langle \mathbf {v} ,\mathbf {v} \rangle }}} .
Natura unui produs scalar presupune că lungimile de vectori pot fi și ele definite, prin definirea normei asociate  | v | := ⟨ v , v ⟩ {\displaystyle |\mathbf {v} |:={\sqrt {\langle \mathbf {v} ,\mathbf {v} \rangle }}} .