Question

The area of the parallelogram represented by the vectors $\overrightarrow{A}=2\hat{i}+3\hat{j}$ and $\overrightarrow{B}=\hat{i}+4\hat{j}$ as its sides is

• A. $15\text{Units}$
• B. $7.5\text{Units}$
• C. $10\text{Units}$
• D. $5\text{Units}$

Answer 1

The correct option is D $5\text{Units}$

$\text{Area of parallelogram}=|\overrightarrow{A}\times \overrightarrow{B}|$
Here $\overrightarrow{A}\times \overrightarrow{B}=(2\hat{i}+3\hat{j})\times (\hat{i}+4\hat{j})$
$\Rightarrow \overrightarrow{A}\times \overrightarrow{B}=8\hat{k}-3\hat{k}$
$\Rightarrow \overrightarrow{A}\times \overrightarrow{B}=5\hat{k}$
$\therefore \text{Magnitude of area}=|\overrightarrow{A}\times \overrightarrow{B}|=5\text{Units}$