If `vecAxxvecB=vecC`, then choose the incorrect option : [`vecA and vecB` are non zero vectors]

Options

A. `vecC` is perpendicular to `(vecA+vecB)`
B. `vecC` is perpendicular to `(vecA-vecB)`
C. `veC` is perpendicular to `(vecAxxvecB)`
D. `vecC` isperpendicular to `vecA` and `vecB`

Explanation

To solve the question, we need to analyze the statement given and the options provided. The question states that if \(\vec{A} \times \vec{B} = \vec{C}\), we need to choose the incorrect option among the following statements:

1. \(\vec{A}\) and \(\vec{B}\) are non-zero vectors.
2. \(\vec{A} + \vec{B}\) is in the same plane as \(\vec{C}\).
3. \(\vec{C}\) is perpendicular to both \(\vec{A}\) and \(\vec{B}\).
4. \(\vec{C}\) has a zero degree angle with itself.

### Step-by-Step Solution:

1. **Understanding the Cross Product**:
The cross product \(\vec{A} \times \vec{B}\) produces a vector \(\vec{C}\) that is perpendicular to both \(\vec{A}\) and \(\vec{B}\). This means that \(\vec{C}\) is not in the same plane as \(\vec{A}\) and \(\vec{B}\) but rather points out of that plane.

2. **Analyzing the Options**:
- **Option 1**: \(\vec{A}\) and \(\vec{B}\) are non-zero vectors.
- This statement is true because for the cross product to be defined and non-zero, both vectors must be non-zero.

- **Option 2**: \(\vec{A} + \vec{B}\) is in the same plane as \(\vec{C}\).
- This statement is incorrect. The vector \(\vec{C}\) (result of \(\vec{A} \times \vec{B}\)) is perpendicular to the plane formed by \(\vec{A}\) and \(\vec{B}\). Thus, \(\vec{A} + \vec{B}\) lies in the plane of \(\vec{A}\) and \(\vec{B}\) and cannot be in the same plane as \(\vec{C}\).

- **Option 3**: \(\vec{C}\) is perpendicular to both \(\vec{A}\) and \(\vec{B}\).
- This statement is true as per the properties of the cross product.

- **Option 4**: \(\vec{C}\) has a zero degree angle with itself.
- This statement is true because any vector has a zero degree angle with itself.

3. **Conclusion**:
The incorrect option among the given statements is **Option 2**.

### Final Answer:
The incorrect option is **Option 2**: \(\vec{A} + \vec{B}\) is in the same plane as \(\vec{C}\).