1. Let $O$ be a point inside $\triangle A B C$, and $\overrightarrow{O A}+2 \overrightarrow{O B}$ $+3 \overrightarrow{O C}=\mathbf{0}$, then the ratio of the area of $\triangle A O C$ to the area of $\triangle B O C$ is $\qquad$
1. Solution: From the given, $\frac{\overrightarrow{O A}}{2}+\overrightarrow{O B}=-\frac{3}{2} \overrightarrow{O C}$, taking the midpoint $M$ of segment $O A$, then the vector $(\overrightarrow{O M}+\overrightarrow{O B})$ is collinear with vector $\overrightarrow{O C}$, so the distances from points $M, B$ to line $O C$ are equal, i.e., the area of $\triangle M O C$ is equal to the area of $\triangle B O C$, thus the ratio of the area of $\triangle A O C$ to the area of $\triangle B O C$ is $2: 1$.