Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogr… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 30 January, Shift 1Cross Product

Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $ABCD$ . If the diagonal $\overrightarrow{BD} = \hat{i} + 2\hat{j} + 3\hat{k}$ , 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
$\frac{1}{2}\sqrt{306}$

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