3d Geometry

Let P be a plane passing through the points (1, 0, 1), (1, \(-\)2, 1) and (0, 1, \(-\)2). Let a vector \(\overrightarrow a = \alpha \widehat i + \beta \widehat j + \gamma \widehat k\) be such that \(\overrightarrow a\) is parallel to the plane P, perpendicular to \((\widehat i + 2\widehat j + 3\widehat k)\) and \(\overrightarrow a \,.\,(\widehat i + \widehat j + 2\widehat k) = 2\), then \({(\alpha - \beta + \gamma )^2}\) equals ____________.