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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 :

$\frac{1}{2} \sqrt{410}$
$\frac{1}{2} \sqrt{306}$
$\frac{1}{2} \sqrt{586}$
$\frac{1}{2} \sqrt{474}$

Solution

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