Vector Algebra

Let \(\overrightarrow a = \widehat i + \widehat j - \widehat k\) and \(\overrightarrow c = 2\widehat i - 3\widehat j + 2\widehat k\). Then the number of vectors \(\overrightarrow b\) such that \(\overrightarrow b \times \overrightarrow c = \overrightarrow a\) and \(|\overrightarrow b | \in\) {1, 2, ........, 10} is :