Final answer:
Without the full expression, it's not possible to definitively choose the mathematical properties needed to rewrite it. For scalar operations, both commutative and associative properties are valid, whereas for vector operations, only the associative property applies due to the anticommutative nature of vector multiplication. Option 3 is correct.
Step-by-step explanation:
The question is asking which mathematical properties could be used to rewrite a given mathematical expression. In general, the commutative property allows us to change the order of the numbers in an operation like addition or multiplication. The associative property allows us to change the grouping of numbers when adding or multiplying without changing the result. These properties do not apply to vector multiplication (cross product), which is anticommutative, and does not possess the commutative property. For scalar multiplication (dot product), both the commutative and associative properties apply.
Based on the provided information and the question context, it seems like the question's full expression is missing, which means we can't concretely determine what properties to apply. However, if the operation was addition or scalar multiplication, we could employ the commutative property or the associative property accordingly. On the other hand, for vector multiplication, only the associative property could be used since the anticommutative property would introduce a minus sign when changing the order.