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
The cross product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is defined as:
\[ \mathbf{A} \times \mathbf{B} = \mathbf{C} \]
where \( \mathbf{C} \) is a vector that is perpendicular to both \( \mathbf{A} \) and \( \mathbf{B} \).

### Step 2: Use the Property of Cross Product
The property of the cross product states that:
\[ \mathbf{B} \times \mathbf{A} = -(\mathbf{A} \times \mathbf{B}) \]
This means that the vector \( \mathbf{B} \times \mathbf{A} \) is equal to the negative of the vector \( \mathbf{A} \times \mathbf{B} \).

### Step 3: Relate the Two Vectors
From the above property, we can write:
\[ \mathbf{B} \times \mathbf{A} = -\mathbf{C} \]
where \( \mathbf{C} = \mathbf{A} \times \mathbf{B} \).

### Step 4: Determine the Direction of the Vectors
Since \( \mathbf{C} \) and \( -\mathbf{C} \) are in opposite directions, we can visualize this:
- \( \mathbf{A} \times \mathbf{B} \) points in one direction.
- \( \mathbf{B} \times \mathbf{A} \) points in the opposite direction.

### Step 5: Find the Angle Between the Vectors
The angle \( \theta \) between two vectors that point in opposite directions is:
\[ \theta = 180^\circ \quad \text{or} \quad \theta = \pi \text{ radians} \]

### Conclusion
Thus, the angle between the vectors \( \mathbf{A} \times \mathbf{B} \) and \( \mathbf{B} \times \mathbf{A} \) is:
\[ \theta = 180^\circ \quad \text{or} \quad \pi \text{ radians} \]

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