Let `vea, vecb and vecc` be unit vectors such that `veca.vecb=0 = veca.vecc`. It the angle between `vecb and vecc is pi/6` then find `veca`.

Explanation

To solve the problem, we need to find the unit vector \(\vec{a}\) given that it is perpendicular to both unit vectors \(\vec{b}\) and \(\vec{c}\), and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\frac{\pi}{6}\).

### Step-by-step Solution:

1. **Understanding the Given Information**:
- We have three unit vectors: \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\).
- The dot products \(\vec{a} \cdot \vec{b} = 0\) and \(\vec{a} \cdot \vec{c} = 0\) imply that \(\vec{a}\) is perpendicular to both \(\vec{b}\) and \(\vec{c}\).
- The angle between \(\vec{b}\) and \(\vec{c}\) is \(\frac{\pi}{6}\).
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