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If the angle between the vectors \( \vec{A} \) and \( \vec{B} \) is \( \theta, \) then the value of the product \( (\vec{B} \times \vec{A}) \cdot \vec{A} \) equals

1. \( B A^{2} \sin \theta \)
2. \( B A^{2} \cos \theta \sin \theta \)
3. \( B A^{2} \cos \theta \)
4. zero

Correct answer: zero

Solution

The vector \(\vec{B} \times \vec{A}\) is perpendicular to \(\vec{A}\) by definition of the cross product. Any vector perpendicular to \(\vec{A}\) has zero dot product with \(\vec{A}\), so the result is zero.

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