Question

The area of the triangle formed by $\hat{i}+2\hat{j}$ and $3\hat{i}+\hat{j}$ is

• A. $3sq.units$
• B. $\frac{1}{2}sq.units$
• C. $2\sqrt{14}sq.units$
• D. $\frac{5}{2}sq.units$

Answer 1

The correct option is D $\frac{5}{2}sq.units$

Let, $\overrightarrow{A}=\hat{i}+2\hat{j},\overrightarrow{B}=3\hat{i}+\hat{j}$
Area of the triangle $=\frac{1}{2}|\overrightarrow{A}\times \overrightarrow{B}|$
$=\frac{1}{2}|(\hat{i}+2\hat{j})\times (3\hat{i}+\hat{j})|$
$=\frac{1}{2}|(\hat{i}\times \hat{j})+(2\hat{j}\times \widehat{3i})|$
$=\frac{1}{2}|\left(\hat{k}\right)-6\hat{k}|=\frac{5}{2}$