请帮我解题，目标群体是初中生---**Extracted Content:** **Question Number:** 15. **Question Stem:** 如图，在四边形ABCD中，∠B = 60°，AB = 3，BC = 6，且 $\vec{AD} = \lambda \vec{BC}$，$\vec{AD} \cdot \vec{AB} = -\frac{3}{2}$。 **Part (1):** 求实数 λ 的值； **Part (2):** 若 M, N 是边 BC 上的动点，且 $|MN| = 1$，求 $\vec{DM} \cdot \vec{DN}$ 的最小值. **Diagram Description:** * **Type:** Geometric figure showing a quadrilateral ABCD with two points M and N on side BC. * **Main Elements:** * **Vertices:** Labeled points A, B, C, D. A is located in the upper left, D in the upper right. B is in the lower left, C in the lower right, forming a base BC. * **Sides:** Lines segments connect A to B, B to C, C to D, and D to A, forming the quadrilateral ABCD. * **Points on BC:** Points M and N are located on the line segment BC. M is positioned to the left of N along BC. * **Lines from D:** Line segments connect point D to points M and N. * **Labels:** Vertices A, B, C, D and points M, N are explicitly labeled. * **Overall Shape:** Appears to be a trapezoid with AD parallel to BC (based on the given condition $\vec{AD} = \lambda \vec{BC}$). BC is the longer base at the bottom, and AD is the shorter base at the top.