Question

Area of $\Delta$ABC(in sq units) is?

• A. $24$
• B. $8\sqrt{6}$
• C. $4\sqrt{6}$
• D. None of these

Answer 1

The correct option is A $24$

$\overrightarrow{AB}=-4\hat{i}+4\hat{j}$

$\overrightarrow{AC}=2\hat{i}+2\hat{j}+2\hat{k}$

$\overrightarrow{AB}.\overrightarrow{BC}=\left|\overrightarrow{AB}\right|\left|\overrightarrow{AC}\right|\cos \theta$

$\Rightarrow \cos \theta =0$

$\theta ={90}^0$

$AB\perp AC$

$\left|\overrightarrow{AC}\right|=\sqrt{12}=2\sqrt{3}$

$\left|\overrightarrow{AB}\right|=\sqrt{32}=4\sqrt{2}$

Area $=\frac{1}{2}\times AB\times AC$

$=\frac{1}{2}\times \sqrt[4]{42}\times \sqrt[2]{23}=\sqrt[4]{46}$ sq. units.