Let $\overrightarrow{a}= 2\hat i +\hat j -2 \hat k$ and $\overrightarrow{b}= \hat i +\hat j $. Let $\overrightarrow{c}$ be a vector such that $\bigg|\overrightarrow{c}-\overrightarrow{a} \bigg|= 3,\bigg|(\overrightarrow{a} \times \overrightarrow{b} ) \times \overrightarrow{c} \bigg|=3$and the angle between $\overrightarrow{c}$ and $\overrightarrow{a} \times \overrightarrow{b}$ be $30^{\circ}$. Then $\overrightarrow{a}.\overrightarrow{c}$ is equal to :
