Question

Prove that the area of the triangle whose adjacent sides are $\overrightarrow{a}=3\hat{i}+4\hat{j}$ and $\overrightarrow{b}=-5\hat{i}+7\hat{j}$ is $20\frac{1}{2}$ square units.

Answer 1

We have $\overrightarrow{a}=3\hat{i}+4\hat{j}$ and $\overrightarrow{b}=-5\hat{i}+7\hat{j}$

$\overrightarrow{a}\times \overrightarrow{b}=a_1{b}_2-a_2{b}_1$

Area of the triangle$=\frac{1}{2}|\overrightarrow{a}\times \overrightarrow{b}|$

Area$=\frac{1}{2}\times (7\times 3+5\times 4)=\frac{41}{2}=20\frac{1}{2}$

Hence, proved.