Let $$\vec{a} = 2\hat{i} + \hat{j} - \hat{k}$$, $$\vec{b} = ((\vec{a} \times (\hat{i} + \hat{j})) \times \hat{i}) \times \hat{i}$$. Then the square of the projection of $$\vec{a}$$ on $$\vec{b}$$ is :

A

$$\frac{1}{3}$$

B

$$\frac{2}{3}$$

C

$$2$$

D

$$\frac{1}{5}$$