Question

If $\overrightarrow{A}$ $=\hat{i}+2\hat{j}+3\hat{k}$ & $\overrightarrow{B}=3\hat{i}-2\hat{j}+\hat{k},$then the area of parallelogram formed with $\overrightarrow{A}and\overrightarrow{B}$ as the sides of the parallelogram is :

• A. $\sqrt{3}$
• B. $8\sqrt{3}$
• C. $64$
• D. $0$

Answer 1

The correct option is B $8\sqrt{3}$

Area of parallelogram

$\overrightarrow{A}\times \overrightarrow{B}=(\hat{i}+2\hat{j}+3\hat{k})\times (3\hat{i}-2\hat{j}+\hat{k})=8\hat{i}+8\hat{j}-8\hat{k}$

magnitude of area

$=\sqrt{64+64+64}=8\sqrt{3}$

Hence (B) option is correct