Lesson 2. How to find an angle between lines || Task #13. Stereometry on the Unified State Exam

Free mini-course "Task #14. How to solve solid geometry on the Unified State Exam in Mathematics." In this lesson, we'll solve more complex problems involving finding the angle between lines. Get the script here: https://vk.com/wall-199104221_59 Subscribe to the VK group: https://vk.com/j_math Lesson #1 "Angle Between Lines":    • Урок 1. Как найти угол между прямыми || За...   Link to the mini-course on constructing sections: https://www.youtube.com/playlist?list.... Timing: 00:00 Introduction 00:24 Problem 1 05:05 Theory 06:26 Problem 2 11:22 Problem 3 16:22 Problem 4 20:36 Problems for independent solution 21:02 Answers and instructions *** Problems: Problem 1. In the unit cube ABCDA1B1C1D1, find the angle between B1D and CD1. Problem 2. In a regular quadrangular pyramid SABCD, all edges of which are equal to 1, point E is the midpoint of edge SC. Find the angle between lines SA and DE. Problem 3. All edges of a regular quadrangular pyramid SABCD are equal. Point M is the midpoint of side BC of the base ABCD, and point N is the midpoint of lateral edge SA. Find the angle between lines SM and BN. Problem 4. In a regular hexagonal pyramid SABCDEF, the base side is equal to 1, and the lateral edge is √3. Point M is the midpoint of edge SC. Find the angle between lines AM and BF. Problem 5. In a regular triangular prism ABCA1B1C1, all edges are equal. Find the angle between AC1 and B1C. Problem 6. In the unit cube ABCDA1B1C1D1, find the angle between AD and A1C. Problem 7. Given a regular quadrangular pyramid SABCD with vertex S, points M and N are the midpoints of edges AB and SC. a) Construct a section of the pyramid by a plane passing through MN parallel to SA. b) Find the angle between lines SA and MN if the lateral edge of the pyramid is equal to the side of the base.