10. Let point $O$ be inside $\triangle A B C$, satisfying
$$
\overrightarrow{O A}+2 \overrightarrow{O B}+3 \overrightarrow{O C}=\mathbf{0} \text {. }
$$

Then the ratio of the area of $\triangle A B C$ to the area of $\triangle A O C$ is $(\quad)$.
(A) 2
(B) 3
(C) $\frac{3}{2}$
(D) $\frac{5}{3}$
10. B.

Take the midpoints $D, E$ of $AC, BC$ respectively.
$$
\begin{array}{l}
\text { By } \overrightarrow{O A}+2 \overrightarrow{O B}+3 \overrightarrow{O C}=\mathbf{0} \\
\Rightarrow \overrightarrow{O A}+\overrightarrow{O C}=-2(\overrightarrow{O B}+\overrightarrow{O C}) \\
\Rightarrow 2 \overrightarrow{O D}=-4 \overrightarrow{O E} \Rightarrow O D=\frac{2}{3} D E \\
\Rightarrow \frac{S_{\triangle A B C}}{S_{\triangle A O C}}=3 .
\end{array}
$$