Vector Algebra: JEE Main 2021 Mathematics question

Let $\overrightarrow a = \widehat i + \alpha \widehat j + 3\widehat k$ and $\overrightarrow b = 3\widehat i - \alpha \widehat j + \widehat k$. If the area of the parallelogram whose adjacent sides are represented by the vectors $\overrightarrow a$ and $\overrightarrow b$ is $8\sqrt 3$ square units, then $\overrightarrow a$ . $\overrightarrow b$ is equal to __________.