Vector Algebra

Let \(\overrightarrow a = \widehat i - \alpha \widehat j + \beta \widehat k\),   \(\overrightarrow b = 3\widehat i + \beta \widehat j - \alpha \widehat k\) and \(\overrightarrow c = -\alpha \widehat i - 2\widehat j + \widehat k\), where \(\alpha\) and \(\beta\) are integers. If \(\overrightarrow a \,.\,\overrightarrow b = - 1\) and \(\overrightarrow b \,.\,\overrightarrow c = 10\), then \(\left( {\overrightarrow a \, \times \overrightarrow b } \right).\,\overrightarrow c\) is equal to ___________.