Vector Algebra

Let O be the origin and \(\overrightarrow {OA} = 2\widehat i + 2\widehat j + \widehat k\) and \(\overrightarrow {OB} = \widehat i - 2\widehat j + 2\widehat k\) and \(\overrightarrow {OC} = {1 \over 2}\left( {\overrightarrow {OB} - \lambda \overrightarrow {OA} } \right)\) for some \(\lambda\) > 0. If \(\left| {\overrightarrow {OB} \times \overrightarrow {OC} } \right| = {9 \over 2}\), then which of the following statements is (are) TRUE?