简要这道题的解析 ---**Extraction Content:** **Question Stem:** 第12题 在△ABC中，AB=2，AC=1，∠BAC = 120°，点E，F在BC边上且 $\vec{BE} = \lambda \vec{BC}$，$\vec{BF} = \mu \vec{BC}$。 **(1)** 若 $\lambda = \frac{1}{3}$，用 $\vec{AB}$，$\vec{AC}$ 表示 $\vec{AE}$，并求线段AE的长； **(2)** 若 $\lambda = \frac{1}{2}$，$\mu = \frac{2}{3}$，求 $\cos \angle EAF$ 的值. **(3)** 若 $\vec{AE} \cdot \vec{AF} = 4$，求 $\frac{1}{\lambda} + \frac{1}{\mu}$ 的值. **Other Relevant Text:** 第5页 **Chart/Diagram Description:** Type: Geometric diagram (Triangle). Main Elements: - Points: Vertices labeled A, B, C. Two points on the side BC labeled E and F. - Lines: Line segments form the sides of the triangle AB, AC, BC. Line segments AE and AF connect vertex A to points E and F on BC. - Shapes: A triangle ABC. - Labels: Points A, B, C, E, F are labeled. - Relative Position and Direction: Point A is at the top vertex. Points B, E, F, C are on the bottom horizontal side in that order from left to right. E and F are between B and C.