If the area of a parallelogram whose diagonals coincide with the following pair of vectors is $5\sqrt{3}$, then vectors are

$\frac{3}{2}\hat i +\frac{1}{2}\hat j-\hat k, 2\hat i-6\hat j + 8\hat k$

If $\vec a, \vec b$ are diagonals of a parallelogram, then its area is $\frac{1}{2}|\vec a×\vec b|$

Clearly, $\frac{1}{2}|\vec a×\vec b|=5\sqrt{3}$ is satisfied by the pair of vectors given in option (2).