Final answer:
The CROSS PRODUCT is non-commutative but distributive over vector addition. Changing the order of vectors produces a vector in the opposite direction due to the anticommutative property.
Step-by-step explanation:
The operation in question is the CROSS PRODUCT, which is a type of vector multiplication. The CROSS PRODUCT is non-commutative, meaning that the order in which two vectors are multiplied affects the result. Specifically, changing the order of the vectors in a cross product will result in their product being pointed in the opposite direction, which is an expression of the anticommutative property. That is, ℓ × B = - (B × ℓ). Furthermore, the CROSS PRODUCT is also distributive over vector addition, which means that A × (B+C) equals A × B + A × C. Unlike the CROSS PRODUCT, other operations such as vector addition and the dot product are commutative, where the order does not affect the outcome.