Question
Let $\vec{a}$, $\vec{b}$, and $\vec{c}$ be unit vectors such that $\vec{a} \cdot \vec{b} = 0 = \vec{a} \cdot \vec{c}$. If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{6}$, then find $\vec{a}$.
Let $\vec{a}$, $\vec{b}$, and $\vec{c}$ be unit vectors such that $\vec{a} \cdot \vec{b} = 0 = \vec{a} \cdot \vec{c}$. If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{6}$, then find $\vec{a}$.