Lines in $mathbf{R}^n$

The line in $mathbf{R}^n$ passing through $x_0 in mathbf{R}^n$ and with direction $u in mathbf{R}^n$ , u ne 0 , is the set of vectors such that x-x_0 is parallel to :

$left{ x_0+t u ~:~ t in mathbf{R} right}.$

We can always assume without loss of generality that the direction is normalized, that is |u|_2 = 1 .

Lines are affine sets of dimension one (since they are translations of the span of one vector).

A line in $mathbf{R}^2$ passing through the point x_0 = (2,0) , with (normalized) direction u = (0.8944,0.4472) .