The dots at the end of [math]\vec{u}[/math] and [math]\vec{v}[/math] may be manipulated. Drag them as you see fit to show how the cross product, [math]\vec{u}\times\vec{v}[/math], changes. (Tapping on a dot directly changes the directions available to move each dot.) [br][br]As you manipulate [math]\vec{u}[/math] and [math]\vec{v}[/math] by moving their respective dots around, please observe the following: [br][br](1) [math]\vec{u}\times\vec{v}[/math] (and [math]\vec{v}\times\vec{u}[/math]) is orthogonal to both [math]\vec{u}[/math] and [math]\vec{v}[/math][br][br](2) [math]\vec{v}\times\vec{u}[/math] points in the opposite direction as [math]\vec{u}\times\vec{v}[/math][br][br](3) The magnitude of [math]\vec{u}\times\vec{v}[/math], denoted [math]\parallel\vec{u}\times\vec{v}\parallel[/math], can be represented by the area of the pink parallelogram.