Let $$\vec{a} = \hat{i} + 4\hat{j} + 2\hat{k}$$, $$\vec{b} = 3\hat{i} - 2\hat{j} + 7\hat{k}$$ and $$\vec{c} = 2\hat{i} - \hat{j} + 4\hat{k}$$. If a vector $$\vec{d}$$ satisfies $$\vec{d} \times \vec{b} = \vec{c} \times \vec{b}$$ and $$\vec{d} \cdot \vec{a} = 24$$, then $$|\vec{d}|^2$$ is equal to

A

$$323$$

B

$$423$$

C

$$313$$

D

$$413$$