Area of parallelogram using vectors.

$1) \text{Find vectors defining parallelogram from one vertex}\\ v_1=(1,1)-(0,2) = (1,-1)\\ v_2=(2,3)-(0,2) = (2,1)\\ 2) \text{augment these to 3D by setting the z coordinate to 0}\\ v_1= (1,-1,0)\\ v_2= (2,1,0)\\ 3) A\hat{k} = v_1 \times v_2\\ \begin{pmatrix}i&j&k\\1&-1&0\\2&1&0\end{pmatrix} = (0, 0,3) = 3\hat{k}\\ A=3$