Let ` vec a , vec b , vec c` be unit vectors such that ` vec adot vec b= vec adot vec c=0` and the angle between ` vec ba n d vec c` is `pi/6`,that `vec a=+-2( vec bxx vec c)dot`

Explanation

To solve the problem step by step, we will analyze the given information and derive the required expression for the vector \(\vec{a}\).

### Step 1: Understand the given conditions
We are given that:
- \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are unit vectors.
- \(\vec{a} \cdot \vec{b} = 0\) and \(\vec{a} \cdot \vec{c} = 0\), which implies 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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