The parallelogram spanned by vectors \(\Vect{a}\) and \(\Vect{b}\) in \(\RNrSpc{n}\) is the collection of all linear combinations \(s\Vect{a}+t\Vect{b}\) with \(0\leq s,t\leq 1\).

\(\ParallelogramOfSet{\Vect{a},\Vect{b}}\)

\(\DefEq \)

\(\SetSlct{\Vect{x}\in\RNrSpc{n}}{ \text{there exist}\quad s,t\in \CCIntrvl{0}{1} \quad\text{for which}\quad \Vect{x}=s\Vect{a} + t\Vect{b} }\)