If the angle between the vectors `vecA and vecB` is `theta,` the value of the product `(vecB xx vecA) * vecA` is equal to

Options

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

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Cross Product**:
The cross product \(\vec{B} \times \vec{A}\) results in a vector that is perpendicular to both \(\vec{B}\) and \(\vec{A}\). The magnitude of this cross product can be expressed as:
\[ |\vec{B} \times \vec{A}| = |\vec{B}| |\vec{A}| \sin(\theta) \]

2. **Direction of the Cross Product**:
The direction of \(\vec{B} \times \vec{A}\) is given by the right-hand rule, and it is perpendicular to the plane formed by \(\vec{A}\) and \(\vec{B}\).

3. **Dot Product with \(\vec{A}\)**:
Now we need to compute the dot product \((\vec{B} \times \vec{A}) \cdot \vec{A}\). Since \(\vec{B} \times \vec{A}\) is perpendicular to \(\vec{A}\), the angle between \(\vec{B} \times \vec{A}\) and \(\vec{A}\) is \(90^\circ\).

4. **Using the Dot Product Formula**:
The dot product of two vectors can be calculated using the formula:
\[ \vec{X} \cdot \vec{Y} = |\vec{X}| |\vec{Y}| \cos(\phi) \]
where \(\phi\) is the angle between the vectors \(\vec{X}\) and \(\vec{Y}\). In our case:
\[ \phi = 90^\circ \implies \cos(90^\circ) = 0 \]

5. **Conclusion**:
Therefore, we have:
\[ (\vec{B} \times \vec{A}) \cdot \vec{A} = |\vec{B} \times \vec{A}| |\vec{A}| \cos(90^\circ) = |\vec{B} \times \vec{A}| |\vec{A}| \cdot 0 = 0 \]
Thus, the value of the product \((\vec{B} \times \vec{A}) \cdot \vec{A}\) is **0**.

### Final Answer:
\[ (\vec{B} \times \vec{A}) \cdot \vec{A} = 0 \]