Question

If the vectors $3\hat{i}+\hat{j}-2\hat{k}$, $\hat{i}-3\hat{j}+4\hat{k}$ are is adjacent sides are $3\hat{i}+\hat{j}-2\hat{k}$, $\hat{i}-3\hat{j}+4\hat{k}$ diagonals of a quadrilateral, then the vector area

• A. $\hat{i}+7\hat{j}-5\hat{k}$
• B. $\hat{i}-7\hat{j}+5\hat{k}$
• C. $-\hat{i}+2\hat{j}+5\hat{k}$
• D. $-\hat{i}-7\hat{j}-5\hat{k}$

Answer 1

The correct option is D $-\hat{i}-7\hat{j}-5\hat{k}$

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

$\overrightarrow{n}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 1& -2\\ 1& -3& 4\end{array}\right|=-2\hat{i}-14\hat{j}-20\hat{k}$
Area vector $=\frac{1}{2}\left(\overrightarrow{n}\right)$

$=-\hat{i}-7\hat{j}-5\hat{k}$