The cross product of two vectors [b]u[/b] and [b]v[/b] in [math]\mathbb{R}^3[/math] is a vector in [math]\mathbb{R}^3[/math] that is perpendicular to both [b]u[/b] and [b]v[/b]. It is denoted [b]u[/b]x[b]v[/b]. Use the applet below to discover the basic properties of the cross product. The questions below the applet are intended to guide your discovery.[br][br]Note: in the applet below, the vectors [b]u[/b] and [b]v[/b] live in [math]\mathbb{R}^3[/math]. The green plane contains the two vectors [b]u[/b] and [b]v[/b] and [b]u[/b]x[b]v[/b] is perpendicular to the green plane. "Up" from the green plane corresponds to "out" of the computer display.