Why is the cross product PERPENDICULAR to both vectors?

The cross product is useful in multivariable calculus and linear algebra primarily because it lets us find a 3D vector that's perpendicular to two vectors we already have. But one thing we often skip over while talking about it is WHY the cross product ends up being perpendicular to its inputs in the first place. Well, here's one way to justify it!

Видео Why is the cross product PERPENDICULAR to both vectors? канала Math with Drew