A line in three-space can be created through a specific point to extend in a particular direction by using scalar multiplication and vector addition.[br][br]When a position vector is added to scalar multiples of a direction vector, the components of the resultant vectors form the set of points making up the line. Initially, a point on the line determines the components of the position vector. A vector parallel to the line is chosen to be the "direction" vector.[br][br][b]Interactive Graph:[/b][br][list][*]Interact with the graph by adjusting the coordinates of points A and B.[/*][*]The [color=#ff0000][b]position vector in red[/b][/color] is [math]\overrightarrow{OA}[/math] and is labeled as [b][color=#ff0000]a[/color][/b].[/*][*]The [b][color=#0000ff]direction vector in blue[/color][/b] is [math]\overrightarrow{AB}[/math] and is labeled as [b][color=#0000ff]b[/color][/b].[/*][*]The parameter is [math]\lambda[/math], which can be varied using the slider.[/*][*]As the parameter λ changes, [math]\vec{r}(\lambda)[/math] = [b][color=#c51414]a[/color][/b] + λ[b][color=#0000ff]b[/color][/b] traces out a line.[/*][/list]