Question

The area of the parallelogram whose diagonals are given by the vectors $3\overrightarrow{i}+\overrightarrow{j}-2\overrightarrow{k}$ and $\overrightarrow{i}-3\overrightarrow{j}+4\overrightarrow{k}$

• A. $10\sqrt3$
• B. $5\sqrt3$
• C. 8
• D. 4

Answer 1

Answer: (B)

Area $=\frac{1}{2} \left|\left(3\,\hat{i}+\hat{j}-2\hat{k}\right)\times\left(\hat{i}-3\,\hat{j}+4\,\hat{k}\right)\right|$
$=\frac{1}{2}\left|-2\,\hat{i}-14\,\hat{j}-10\,\hat{k}\right|$
$=\frac{\sqrt{4+196+100}}{2}$
$=\frac{10\sqrt{3}}{2}=5\sqrt{3}$