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 $$\overrightarrow{OC} = \frac{1}{2}(\overrightarrow{OB} −\lambda\overrightarrow{OA})$$ for some $$\lambda > 0$$. If $$|\overrightarrow{OB} \times \overrightarrow{OC}| = \frac{9}{2}$$, then which of the following statements is (are) TRUE ?

A

Projection of $$\overrightarrow{OC}$$ on $$\overrightarrow{OA}$$ is $$-\frac{3}{2}$$

B

Area of the triangle OAB is $$\frac{9}{2}$$

C

Area of the triangle ABC is $$\frac{9}{2}$$

D

The acute angle between the diagonals of the parallelogram with adjacent sides $$\overrightarrow{OA}$$ and $$\overrightarrow{OC}$$ is $$\frac{\pi}{3}$$