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

Answer 1

The correct option is B $\sqrt{171}\text{units}$

$\overrightarrow{A}\times \overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 5& -4& 3\\ 3& 2& -1\end{array}\right|=-2\hat{i}+14\hat{j}+22\hat{k}$

Area of parallelogram $=\frac{1}{2}|\overrightarrow{A}\times \overrightarrow{B}|=\sqrt{1^2+7^2+{11}^2}=\sqrt{171}\text{units}$