જો $\vec{a} = 2\hat{i} + \hat{j} + \hat{k}$,$\vec{b} = \hat{i} + 2\hat{j} + 2\hat{k}$,$\vec{c} = \hat{i} + \hat{j} + 2\hat{k}$ અને $(1 + \alpha)\hat{i} + \beta(1 + \alpha)\hat{j} + \gamma(1 + \alpha)(1 + \beta)\hat{k} = \vec{a} \times (\vec{b} \times \vec{c})$ હોય,તો $\alpha, \beta, \gamma$ ની કિંમત શોધો.

• A
  $-2, -4, -\frac{2}{3}$
• B
  $2, -4, \frac{2}{3}$
• C
  $-2, 4, \frac{2}{3}$
• D
  $2, 4, -\frac{2}{3}$