If `vecA` and `vecB` are two vectors, then which of the following is wrong?

Options

A. `vecA + vecB = vecB + vecA`
B. `vecA * vecB = vecB * vecA`
C. `vecA xx vecB = vecB xx vecA`
D. `vecA - vecB = - (vecB - vecA)`

Explanation

To solve the question, we need to analyze the properties of vector addition, scalar and vector multiplication, and subtraction. Let's go through each option step by step.

### Step 1: Analyze the first option
The first option states that \( \vec{A} + \vec{B} = \vec{B} + \vec{A} \).
- This is true because vector addition is commutative. It means that the order in which you add vectors does not matter.

### Step 2: Analyze the second option
The second option states that \( \vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A} \).
- This is also true because the dot product (scalar product) of two vectors is commutative. The result remains the same regardless of the order of the vectors.

### Step 3: Analyze the third option
The third option states that \( \vec{A} \times \vec{B} = \vec{B} \times \vec{A} \).
- This is false because the cross product (vector product) of two vectors is not commutative. In fact, \( \vec{A} \times \vec{B} = -(\vec{B} \times \vec{A}) \). Therefore, this statement is incorrect.

### Step 4: Analyze the fourth option
The fourth option states that \( \vec{A} - \vec{B} = -\vec{B} + \vec{A} \).
- This is true because vector subtraction can be rewritten as addition of the negative vector. Thus, \( \vec{A} - \vec{B} \) can be expressed as \( -\vec{B} + \vec{A} \).

### Conclusion
Based on the analysis:
- The first option is correct.
- The second option is correct.
- The third option is incorrect (this is the wrong statement).
- The fourth option is correct.

Thus, the answer to the question is that the third statement is wrong.