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[[File:Line equation qtl4.svg|thumb|Planar [[analytic geometry]] uses the coordinate space '''R'''<sup>2</sup>. ''Depicted:'' description of a [[line (geometry)|line]] as the [[equation solving#Solution sets|solution set]] in <math>\vec x</math> of the vector equation <math>\vec x \cdot \vec n = d</math>.]]
{{Main|Coordinate space}}
The original example of a vector space is the following. For any [[Positive number|positive]] [[integer]] ''n'', the [[Set (mathematics)|set]] of all ''n''-tuples of elements of ''F'' forms an ''n''-dimensional vector space over ''F'' sometimes called ''[[coordinate space]]'' and denoted ''F''<sup>''n''</sup>.<ref>{{Harvard citations|last = Lang|year = 1987|loc = ch. I.1|nb = yes}}</ref> An element of ''F''<sup>''n''</sup> is written
:<math>x = (x_1, x_2, \ldots, x_n) </math>
where each ''x''<sub>''i''</sub> is an element of ''F''. The operations on ''F''<sup>''n''</sup> are defined by
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