# Function CROSS

## Slots on this function:

Documentation:
Vector or cross product of two three dimensional vectors. If we know the components of two vectors with respect to a common basis, we can determine the components of the cross product in that basis.
Arity: 3

## Axioms:

```(Nth-Domain Cross 3 3d-Vector-Quantity)

(Nth-Domain Cross 2 3d-Vector-Quantity)

(Nth-Domain Cross 1 3d-Vector-Quantity)

(<=> (Cross ?V1 ?V2 ?V)
(And (3d-Vector-Quantity ?V1)
(3d-Vector-Quantity ?V2)
(3d-Vector-Quantity ?V)
(= (Quantity.Dimension ?V)
(* (Quantity.Dimension ?V1) (Quantity.Dimension ?V2)))
(= (Dot ?V1 ?V)
(The-Zero-Scalar-For-Dimension (* (Quantity.Dimension ?V1)
(Quantity.Dimension ?V))))
(= (Dot ?V2 ?V)
(The-Zero-Scalar-For-Dimension (* (Quantity.Dimension ?V2)
(Quantity.Dimension ?V))))
(= (Vector-Component ?V 1 ?B)
(- (* (Vector-Component ?V1 2 ?B)
(Vector-Component ?V2 3 ?B))
(* (Vector-Component ?V2 2 ?B)
(Vector-Component ?V1 3 ?B))))
(= (Vector-Component ?V 2 ?B)
(- (* (Vector-Component ?V2 1 ?B)
(Vector-Component ?V1 3 ?B))
(* (Vector-Component ?V1 1 ?B)
(Vector-Component ?V2 3 ?B))))
(= (Vector-Component ?V 3 ?B)
(- (* (Vector-Component ?V1 1 ?B)
(Vector-Component ?V2 2 ?B))
(* (Vector-Component ?V2 1 ?B)
(Vector-Component ?V1 2 ?B))))))

```