If `vec(A)` and `vec(B)` are two vectors, which of the following is not correct?

Options

A. `vec(A)+vec(B)= vec(B)+vec(A)`
B. `vec(A).vec(B)= vec(B).vec(A)`
C. `vec(A)xxvec(B)= vec(B)xxvec(A)`
D. `vec(A)-vec(B)= -(vec(B)-vec(A))`

Explanation

To determine which statement about the vectors \(\vec{A}\) and \(\vec{B}\) is not correct, let's analyze each option step by step.

### Step 1: Analyze the first option
**Statement:** \(\vec{A} + \vec{B} = \vec{B} + \vec{A}\)

- This statement represents the commutative property of vector addition.
- Vectors can be added in any order, so this statement is **correct**.

### Step 2: Analyze the second option
**Statement:** \(\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}\)

- This statement represents the commutative property of the dot product.
- The dot product of two vectors is also commutative, so this statement is **correct**.

### Step 3: Analyze the third option
**Statement:** \(\vec{A} \times \vec{B} = \vec{B} \times \vec{A}\)

- This statement represents the cross product of two vectors.
- The cross product is not commutative; in fact, \(\vec{A} \times \vec{B} = -(\vec{B} \times \vec{A})\).
- Therefore, this statement is **not correct**.

### Step 4: Analyze the fourth option
**Statement:** \(\vec{A} - \vec{B} = -\vec{A} + \vec{B}\)

- This statement can be rearranged to show that \(\vec{A} - \vec{B} = -(\vec{B} - \vec{A})\), which is a valid representation of vector subtraction.
- Thus, this statement is **correct**.

### Conclusion
The statement that is **not correct** is:
\[ \vec{A} \times \vec{B} = \vec{B} \times \vec{A} \]