This applet shows a line in ℝ[sup]2[/sup] and the vector form of its equation.[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]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.