Let $$A(2, 3, 5)$$ and $$C(-3, 4, -2)$$ be opposite vertices of a parallelogram $$ABCD$$ if the diagonal $$\vec{BD} = \hat{i} + 2\hat{j} + 3\hat{k}$$ then the area of the parallelogram is equal to

A

$$\frac{1}{2}\sqrt{410}$$

B

$$\frac{1}{2}\sqrt{474}$$

C

$$\frac{1}{2}\sqrt{586}$$

D

$$\frac{1}{2}\sqrt{306}$$