If you have two vectors on a grid, you can move the tail of each vector to the point of the other vector and draw out a parallelogram. The “Cross Product” is the area of this parallelogram. However, what is interesting, is that order matters. If you switch the order in which one vector is pushed to the edge of the order vector, the parallelogram is flipped, and in this case the area will be negative.
Connections
The Determinate Of A Matrix Measures The Change In Area Of A Square On A Grid
Link Explanation: This is a fundamental connection. The determine is the area of the cross product between two vectors. If you take the two vectors and turn them into a single matrix, you can then achieve the area of that matrix by calculating the determinate, as described in the note above.
Reference
https://www.youtube.com/watch?v=eu6i7WJeinw&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=10