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