Question

The area of the triangle formed by $2\hat{i}+\hat{j}$ and $\hat{i}+\hat{j}$ is

• A. $3\text{sq. units}$
• B. $\frac{1}{2}\text{sq. units}$
• C. $2\sqrt{14}\text{sq. units}$
• D. $\frac{\sqrt{14}}{2}\text{sq. units}$

Answer 1

The correct option is B $\frac{1}{2}\text{sq. units}$

$\overrightarrow{A}=2\hat{i}+\hat{j},\overrightarrow{B}=\hat{i}+\hat{j}$
Area of the triangle = $\frac{1}{2}|\overrightarrow{A}\times \overrightarrow{B}|$
$=\frac{1}{2}|(2\hat{i}+\hat{j})\times (\hat{i}+\hat{j})|$
$=\frac{1}{2}|2\hat{k}+(-\hat{k})|$
$=\frac{1}{2}\hat{k}$