Answer
$\frac{3}{2}$
Work Step by Step
We have $\vec{AB}= -\hat{i}+2\hat{j}$
and $\vec{AC}= -\hat{i}-\hat{j}$.
Now, $\vec{AB}\times\vec{AC}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\-1&2&0\\-1&0&-1\end{vmatrix}$$=-2\hat{i}+\hat{j}+2\hat{k}$.
Therefore, $|\vec{AB}\times\vec{AC}|=\sqrt {4+1+4}= 3$.
The area of the given triangle= $\frac{1}{2}|\vec{AB}\times\vec{AC}|=\frac{3}{2}$
