Question

The area of the parallelogram having diagonals $3\hat{i}+\hat{j}-2\hat{k}$ and $\hat{i}-3\hat{j}+4\hat{k}$ is

• A. $5\sqrt{3}$
• B. $3\sqrt{3}$
• C. $2\sqrt{3}$
• D. $3\sqrt{5}$

Answer 1

The correct option is A $5\sqrt{3}$

Area of Parallelogram $=\frac{1}{2}|\overrightarrow{n}|$

$\overrightarrow{n}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 1& -2\\ 1& -3& 4\end{array}\right|=-2\hat{i}-14\hat{j}-10\hat{k}$

Area of Parallelogram $=\frac{1}{2}\times 10\sqrt{3}$

$=5\sqrt{3}$