Is there a connection between cross product and determinant?

[kidsasd987]

Is this just a coincidence that cross product can be found from determinant of 3*3 matrix? what is the differences between wedge product and cross product?Thanks.

 

[Simon Bridge]

Is this just a coincidence that cross product can be found from determinant of 3*3 matrix?

No.
It is another way of writing the definition.

what is the differences between wedge product and cross product?

https://www.physicsforums.com/threads/wedge-product-cross-product.117231/
Basically the wedge product is a generalization of the cross-product to any vector space.

 

[WWGD]

For one, the wedge product is defined on forms, and the cross-product is defined on vectors.