If `vec(A)xxvec(B)=vec(B)xxvec(A)`, then the angle between `vec(A)` and `vec(B)` is-

Options

A. `pi`
B. `pi//3`
C. `pi//2`
D. `pi//4`

Explanation

To solve the problem, we need to analyze the given equation:

\[ \vec{A} \times \vec{B} = \vec{B} \times \vec{A} \]

1. **Understanding the Cross Product**:
The cross product of two vectors \(\vec{A}\) and \(\vec{B}\) is defined as:
\[ \vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin(\theta) \hat{n} \]
where \(\theta\) is the angle between the two vectors and \(\hat{n}\) is the unit vector perpendicular to the plane formed by \(\vec{A}\) and \(\vec{B}\).

2. **Using the Anticommutative Property**:
The cross product has an anticommutative property, which means:
\[ \vec{B} \times \vec{A} = -(\vec{A} \times \vec{B}) \]
This implies that:
\[ \vec{A} \times \vec{B} = -(\vec{A} \times \vec{B}) \]

3. **Setting the Equations Equal**:
Given that \(\vec{A} \times \vec{B} = \vec{B} \times \vec{A}\), we can substitute from the anticommutative property:
\[ \vec{A} \times \vec{B} = -(\vec{A} \times \vec{B}) \]

4. **Simplifying the Equation**:
If we add \(\vec{A} \times \vec{B}\) to both sides, we get:
\[ 2(\vec{A} \times \vec{B}) = 0 \]
This means:
\[ \vec{A} \times \vec{B} = 0 \]

5. **Interpreting the Result**:
The condition \(\vec{A} \times \vec{B} = 0\) implies that the vectors \(\vec{A}\) and \(\vec{B}\) are parallel or antiparallel. This occurs when the angle \(\theta\) between them is either \(0\) degrees or \(180\) degrees.

6. **Conclusion**:
Therefore, the angle between \(\vec{A}\) and \(\vec{B}\) is:
\[ \theta = 0 \text{ or } 180 \text{ degrees} \]

### Final Answer:
The angle between \(\vec{A}\) and \(\vec{B}\) is \(180^\circ\).