Question

A parallelogram has diagonals expressed as $\overrightarrow{A}=5\hat{i}-4\hat{j}+3\hat{k}$ and $\overrightarrow{B}=3\hat{i}+2\hat{j}-\hat{k}$. Area of parallelogram is:

• A. $\sqrt{117}$ units
• B. $\sqrt{171}$ units
• C. $\sqrt{711}$ units
• D. $\sqrt{107}$ units

Answer 1

Answer: (B)

$\sqrt{171}$ units

$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 5& -4& 3\\ 3& 2& -1\end{array}\right|$
$\overrightarrow{A}\times \overrightarrow{B}=-2\hat{i}+14\hat{j}+22\hat{k}$
Area $=\frac{1}{2}|\overrightarrow{A}\times \overrightarrow{B}|=\sqrt{(-1{)}^2+7^2+{11}^2}=\sqrt{171}$ unit