2. Given points $A(0,2,3)$, $B(-2,1,6)$, $C(1,-1,5)$.
(1) Find the area of the parallelogram with sides $\overrightarrow{A B}$ and $\overrightarrow{A C}$;
(2) If $|\vec{a}|=\sqrt{3}$, and $\vec{a}$ is perpendicular to both $\overrightarrow{A B}$ and $\overrightarrow{A C}$, find the coordinates of vector $\vec{a}$.
2. (1) $\overrightarrow{A B}=\{-2,-1,3\}, \overrightarrow{A C}=\{1,-3,2\}, \cos \theta=\frac{\overrightarrow{A B} \cdot \overrightarrow{A C}}{|\overrightarrow{A B}||\overrightarrow{A C}|}=\frac{1}{2}, \sin \theta=$ $\frac{\sqrt{3}}{2}, S=|\overrightarrow{A B}| \cdot|\overrightarrow{A C}| \sin \theta=\sqrt{14} \cdot \sqrt{14} \cdot \frac{\sqrt{3}}{2}=7 \sqrt{3} ;$
(2) Let $\vec{a}=\{x, y, z\}$. From $\overrightarrow{A B} \cdot \vec{a}=0, \overrightarrow{A C} \cdot \vec{a}=0$ we get