If the angle between the vectors A and B is `theta`, the value of the product (BxA). A is equal to

Options

A. `BA^(2)cos theta`
B. `BA^(2) sin theta`
C. `BA^(2) sin theta cos theta`
D. zero

Answer

To solve the problem, we need to find the value of the product \( \mathbf{B} \times \mathbf{A} \) when the angle between the vectors \( \mathbf{A} \) and \( \mathbf{B} \) is \( \theta \).

### Step-by-Step Solution:

1. **Understand the Cross Product**: The cross product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is given by the formula:
\[ \mathbf{A} \times \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \sin(\theta) \, \mathbf{n} \]
where \( |\mathbf{A}| \) and \( |\mathbf{B}| \) are the magnitudes of vectors \( \mathbf{A} \) and \( \mathbf{B} \), \( \theta \) is the angle between them, and \( \mathbf{n} \) is the unit vector perpendicular to the plane formed by \( \mathbf{A} \) and \( \mathbf{B} \).

2. **Identify the Angle**: In this case, we are given that the angle between the vectors \( \mathbf{A} \) and \( \mathbf{B} \) is \( \theta \).

3. **Calculate the Magnitude of the Cross Product**: The magnitude of the cross product \( \mathbf{B} \times \mathbf{A} \) can be calculated using the same formula:
\[ |\mathbf{B} \times \mathbf{A}| = |\mathbf{B}| |\mathbf{A}| \sin(\theta) \]

4. **Direction of the Cross Product**: The direction of \( \mathbf{B} \times \mathbf{A} \) is given by the right-hand rule, which means it is perpendicular to both \( \mathbf{B} \) and \( \mathbf{A} \).

5. **Conclusion**: The value of \( \mathbf{B} \times \mathbf{A} \) is a vector that has a magnitude of \( |\mathbf{B}| |\mathbf{A}| \sin(\theta) \) and is directed perpendicular to the plane formed by \( \mathbf{A} \) and \( \mathbf{B} \).

### Final Result:
Thus, the value of the product \( \mathbf{B} \times \mathbf{A} \) is:
\[ \mathbf{B} \times \mathbf{A} = |\mathbf{B}| |\mathbf{A}| \sin(\theta) \, \mathbf{n} \]