This applet shows a line in ℝ[sup]3[/sup] and the vector form of its equation. [br][br][br]A vector equation for a line has the form [b]r[/b] = [b]r[/b][sub]0[/sub] + t[b]v[/b], t ∈ ℝ where [b]r[/b][sub]0[/sub] is the position vector of a point on the line, and [b]v[/b] is a vector parallel to the line. [br][br]You can click and drag [b]r[/b][sub]0[/sub] and [b]v[/b] to adjust the line. [br][br]Try modifying both [b]r[/b][sub]0[/sub] and [b]v[/b] in turn, to see what the resulting lines have in common.[br][br]By default you can only move the points horizontally (parallel to the xy-plane); if you wish to switch between moving the points horizontally or vertically, click on the point a second time. [br][br]If you select the "Constrain points to line" checkbox, the line will be locked in place, and [b]r[/b][sub]0[/sub] and [b]v[/b] will only be able to be moved along the line. This allows you to see that the same line can have many possible vector equations.