Question

Calculate the area of the triangle determined by the two vectors : $\overrightarrow{A}=3\hat{i}+4\hat{j}$ and $\overrightarrow{B}=-3\hat{i}+7\hat{j}$.

Answer 1

Area of the triangle determined by the two vectors $=\frac{1}{2}|\overrightarrow{A}\times \overrightarrow{B}|$

$=\frac{1}{2}|(3\hat{i}+4\hat{j})\times (-3\hat{i}+7\hat{j})|$

$=\frac{1}{2}|21\hat{k}-12(-\hat{k})|$

$=\frac{1}{2}|33\hat{k}|$

$=16.5$ square unit