Question

Let \( \vec{a}, \vec{b}, \vec{c} \) be unit vectors. Suppose \( \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0 \) and the angle between \( \vec{b} \) and \( \vec{c} \) is \( \frac{\pi}{6} \). Then \( \vec{a} \) is:

• A. \( \vec{b} \times \vec{c} \)
• B. \( \vec{c} \times \vec{b} \)
• C. \( \vec{b} + \vec{c} \)
• D. \( \pm 2 (\vec{b} \times \vec{c}) \)

Hint:

For unit vectors, use the cross product to find a vector perpendicular to two given vectors, and adjust the scalar to match the unit vector condition. The magnitude of \( \vec{b} \times \vec{c} \) depends on the angle between \( \vec{b} \) and \( \vec{c} \).