Vector Algebra

If \(\overrightarrow a = \widehat i + 2\widehat k,\overrightarrow b = \widehat i + \widehat j + \widehat k,\overrightarrow c = 7\widehat i - 3\widehat j + 4\widehat k,\overrightarrow r \times \overrightarrow b + \overrightarrow b \times \overrightarrow c = \overrightarrow 0\) and \(\overrightarrow r \,.\,\overrightarrow a = 0\). Then \(\overrightarrow r \,.\,\overrightarrow c\) is equal to :