Cross Product 2D Formula
The cross product of two vectors is equal to the signed area of the parallelogram between them. For example, given the vectors and the cross product is equal to .
We visualize the cross product as the signed area of the parallelogram between the two vectors. When the second vector a counterclockwise rotation away from first vector, the area is positive.
When the second vector a clockwise rotation away from first vector, the area is negative. We can visualize the negative case in this example by switching the order of the vectors in the cross product.
The cross product of two vectors in three dimensions produces a vector perpendicular to the two vectors and whose length is eual to the area betwee the two vectors.