Question

The area of the triangle formed by the points $A(1,2,3)$ , $B(2,3,1)$ , $C(3,1,2)$ is

• A. $\frac{3\sqrt{3}}{2}$
• B. $3\sqrt{3}$
• C. $\sqrt{3}/2$
• D. $\sqrt{3}$

Answer 1

The correct option is A $\frac{3\sqrt{3}}{2}$

$\overrightarrow{AB}=(1,1,-2)$
$\overrightarrow{AC}=(2,-1,-1)$
$\overrightarrow{n}=\overrightarrow{AB}\times \overrightarrow{AC}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 1& -2\\ 2& -1& -1\end{array}\right|=-3\hat{i}-3\hat{j}-3\hat{k}$
Area of $\Delta =\frac{1}{2}|\overrightarrow{n}|$
$=\frac{3\sqrt{3}}{2}$