Thank you for reporting, we will resolve it shortly
Q.
The diagonals of a parallelogram are the vectors $3 \hat{i}+6 \hat{j}-2 \hat{k}$ and $-\hat{i}-2 \hat{j}-8 \hat{k}$ then the length of the shorter side of parallelogram is at.-
$\overline{ a }=\frac{\overline{ d }_{1}+\overline{ d }_{2}}{2}=\frac{2 i +4 j -10 k }{2}$
$= i +2 j -5 k$
$|\overline{ a }|=\sqrt{30}$
$|\overline{ b }|=\frac{\overline{ d }_{1}-\overline{ d }_{2}}{2}=\frac{4 i +8 j +6 k }{2}$
$=2 i +4 j +3 k$
$|\overline{ b }|=\frac{2}{\sqrt{4+16+9}}=\sqrt{29}$