1. In $\triangle A B C$, $|\overrightarrow{A B}|=2,|\overrightarrow{A C}|=3, \overrightarrow{A B} \cdot \overrightarrow{C A}>0$, and the area of $\triangle A B C$ is $\frac{3}{2}$, then $\angle B A C$ equals
A. $150^{\circ}$
B. $30^{\circ}$
C. $120^{\circ}$
D. $60^{\circ}$
Answer
Since $\sin \angle B A C=\frac{1}{2}$ and $\angle B A C$ is an obtuse angle $\Rightarrow \angle B A C=150^{\circ}$, so the answer is $A$.