Question

Two adjacent sides of a parallelogram are represented by the two vectors $\hat{i}+2\hat{j}+3\hat{k}$ and $3\hat{i}-2\hat{j}+\hat{k}$. What is the area of parallelogram ?

• A. $8\text{units}$
• B. $8\sqrt{3}\text{units}$
• C. $3\sqrt{8}\text{units}$
• D. $192\text{units}$

Answer 1

The correct option is A $8\text{units}$

Area of parallelogram $=|\overrightarrow{A}\times \overrightarrow{B}|$
Now $\overrightarrow{A}\times \overrightarrow{B}=(\hat{i}+2\hat{j}+3\hat{k})\times (3\hat{i}-2\hat{j}+\hat{k})$
$\overrightarrow{A}\times \overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 2& 3\\ 3& -2& 1\end{array}\right|=\left(8\right)\hat{i}+\left(8\right)\hat{j}-\left(8\right)\hat{k}$
Magnitude $=\sqrt{64+64+64}=8\sqrt{3}$