Question

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.-

• A. $2\sqrt{3}$
• B. $\sqrt{14}$
• C. $\sqrt{29}$
• D. $4\sqrt{3}$

Answer 1

Answer: (C)

$\overline{a}=\frac{{\overline{d}}_1+{\overline{d}}_2}{2}=\frac{2i+4j-10k}{2}$
$=i+2j-5k$
$|\overline{a}|=\sqrt{30}$
$|\overline{b}|=\frac{{\overline{d}}_1-{\overline{d}}_2}{2}=\frac{4i+8j+6k}{2}$
$=2i+4j+3k$
$|\overline{b}|=\frac{2}{\sqrt{4+16+9}}=\sqrt{29}$