This applet shows a plane in ℝ[sup]3[/sup] and the vector form of its equation. [br][br]A vector equation for a plane has the form [b]r[/b] = [b]r[/b][sub]0[/sub] + s[b]u[/b] + t[b]v[/b], s,t ∈ ℝ where [b]r[/b][sub]0[/sub] is the position vector of a point on the plane, and [b]u[/b] and [b]v[/b] are vectors parallel to the plane. [br][br]You can click and drag [b]r[/b][sub]0[/sub], [b]u[/b] and [b]v[/b] to adjust the plane. [br][br]Try modifying each of the vectors in turn, to see what the resulting planes and their normal vectors 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 plane" checkbox, the plane will be locked in place, and [b]r[/b][sub]0[/sub], [b]u[/b] and [b]v[/b] will only be able to be moved within the plane. This allows you to see that the same plane can have many possible vector equations.