帮我解答一下这道几何图形题---Here is the extracted content from the image: **Problem 17:** **(24-25高二·下·山西·某中学期中)** **Question Stem:** 如图, 四棱柱ABCD - A1B1C1D1的棱长均为2, 且BD = 2, cos∠A1AB = 1/4, cos∠A1AD = 3/4. E是A1C1中点. (1)求证: 平面A1BD ⊥ 平面ABCD; (2)求二面角A1 - BC - E的余弦值. **Chart/Diagram Description:** * **Type:** 3D geometric figure (quadrangular prism). * **Main Elements:** * A quadrangular prism labeled ABCD on the bottom face and A1B1C1D1 on the top face, such that AA1, BB1, CC1, DD1 are the vertical edges. * Vertices are labeled A, B, C, D on the bottom plane and A1, B1, C1, D1 on the top plane. * Edges of the bottom face ABCD are connected. Edges of the top face A1B1C1D1 are shown with some dashed lines (A1D1, C1D1, B1C1). * Vertical edges AA1, BB1, CC1, DD1 are drawn. * Diagonals A1B, A1D, and BD are drawn on the bottom face or connecting A1 to the bottom face. * Point E is marked as the midpoint of the diagonal A1C1 on the top face. * Dashed lines represent hidden edges (AD, CD, A1D1, C1D1, B1C1, B1D1, A1C1). * Solid lines represent visible edges (AB, BC, AA1, BB1, CC1, DD1, A1B, A1D, BD, BE, CE). Note: BE and CE appear to be drawn in the figure, connecting B to E and C to E. **Problem 18:** **(2025·上海长宁·二模)** **Question Stem:** 为响应国家促进消费的政策, 某大型商场举办了“消费满减乐翻天”的优惠活动, 顾客消费满 800 元 (含 800元) 可抽奖一次, 抽奖方案有两种 (顾客只能选择其中的一种). 方案 1: 从装有 5 个红球, 3 个蓝球 (形状、大小完全相同) 的抽奖盒中, 有放回地依次摸出 3 个球. 每摸出 1 次红球, 则额外再减 200 元 (即总共减 650 元); (Incomplete text - seems to describe the reward for getting red balls in Scheme 1) 方案 2: 从装有... (Incomplete text - description of Scheme 2 is cut off) **Options:** * No options provided in the image.