Question

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

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

Answer 1

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

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