Question

In a $△ABC,AB=ri+j,AC=si-j$ if the area of triangle is of unit magnitude, then

• A. $|r-s|=2$
• B. $|r+s|=1$
• C. $|r+s|=2$
• D. $|r-s|=1$

Answer 1

Answer: (C)

$|r+s|=2$

Area of $△ABC=\frac{1}{2}|\overline{AB}\times \overline{AC}|=1$ (given)
$\Rightarrow |\overline{AB}\times \overline{AC}|=2$
$\Rightarrow |r(\hat{i}+\hat{j})\times (s\hat{i}-\hat{j})|=2$
$\Rightarrow |(-r)(\hat{i}\times \hat{j})+s(\hat{j}\times \hat{i})|=3$
$\Rightarrow |-(r+s)\hat{k}|=2$
$\Rightarrow |r+s|=2$.