JEE Math Practice Question
Let $$A(2,3,5)$$ and $$C(-3,4,-2)$$ be opposite vertices of a parallelogram $$A B C D$$. If the diagonal $$\overrightarrow{\mathrm{BD}}=\hat{i}+2 \hat{j}+3 \hat{k}$$, then the area of the parallelogram is equal to :
- A.$$\frac{1}{2} \sqrt{410}$$
- B.$$\frac{1}{2} \sqrt{306}$$
- C.$$\frac{1}{2} \sqrt{586}$$
- D.$$\frac{1}{2} \sqrt{474}$$
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