Cross Product and Area Visualization
Vectors and are shown in 2 and 3 dimensions, respectively. You can drag points B and C to change these vectors. Note: in the 3D view, click on the point twice in order to change its z-coordinate. As you change these vectors, observe how the cross product (the vector in red), , changes. Notice that the magnitude of the cross product is always the same as the area of the parallelogram spanned by and .