Question

The Vector area of the parallelogram whose adjacent sides are $3\hat{i}+\hat{j}-2\hat{k}$ and $\hat{i}-3\hat{j}+4\hat{k}$.

• A. $2\hat{i}+14\hat{j}-10\hat{k}$
• B. $2\hat{i}-14\hat{j}+10\hat{k}$
• C. $-2\hat{i}+4\hat{j}+10\hat{k}$
• D. $-2\hat{i}-14\hat{j}-10\hat{k}$

Answer 1

Answer: (D)

$-2\hat{i}-14\hat{j}-10\hat{k}$

Adjacent side are
$3\hat{i}+\hat{j}-2\hat{k},\hat{i}-3\hat{j}+4\hat{k}$

$\overrightarrow{n}=(3\hat{i}+\hat{j}-2\hat{k})\times (\hat{i}-3\hat{j}+4\hat{k})$

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