The angle between vectors `(AxxB)and(BxxA)` is

Explanation

To find the angle between the vectors \( \mathbf{A} \times \mathbf{B} \) and \( \mathbf{B} \times \mathbf{A} \), we can follow these steps:

### Step 1: Understand the Cross Product Properties
The cross product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) has a specific property:
\[ \mathbf{A} \times \mathbf{B} = -(\mathbf{B} \times \mathbf{A}) \]
This means that the vector \( \mathbf{B} \times \mathbf{A} \) is equal in magnitude to \( \mathbf{A} \times \mathbf{B} \) but points in the opposite direction.

### Step 2: Visualize the Vectors
When we visualize the vectors \( \mathbf{A} \times \mathbf{B} \) and \( \mathbf{B} \times \mathbf{A} \), we see that they are equal in magnitude but opposite in direction. This can be represented as:
\[ \mathbf{B} \times \mathbf{A} = -(\mathbf{A} \times \mathbf{B}) \]

### Step 3: Determine the Angle Between the Vectors
The angle \( \theta \) between two vectors can be determined using the dot product formula:
\[ \cos(\theta) = \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}||\mathbf{B}|} \]
However, since we know that \( \mathbf{B} \times \mathbf{A} \) is in the opposite direction of \( \mathbf{A} \times \mathbf{B} \), we can directly conclude that the angle between them is:
\[ \theta = 180^\circ \]

### Conclusion
Thus, the angle between the vectors \( \mathbf{A} \times \mathbf{B} \) and \( \mathbf{B} \times \mathbf{A} \) is \( 180^\circ \).

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