JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 84

Let $\vec a=2\hat i+\hat j-2\hat k$ and $\vec b=\hat i+\hat j$. Let $\vec c$ be a vector such that $|\vec c-\vec a|=3$, $\left|(\vec a\times\vec b)\times\vec c\right|=3$ and the angle between $\vec c$ and $\vec a\times\vec b$ be 30°. Then $\vec a\cdot\vec c$ is equal to :