Stereometry from scratch to the level of the Unified State Exam. Coordinate-vector method. Problems for proof
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Summer school and annual courses for the Unified State Exam 2025 with a mathematician from Moscow State University: https://3.shkolkovo.online/math-msu My Telegram channel: https://t.me/mathmsu Materials for the intensive course SIROP are here: https://mnlp.cc/mini?domain=mathmsu&i... If you are in the 10th grade, then this is where you should go: https://t.me/+yeAlGTQAn5E0ZmZi Everything about the Moscow State University DWI is here: https://t.me/+hNmZJa59rY9hMjli VK group: https://vk.com/hitman_math Tik-Tok: / hitman_math My Instagram: / andreypavlikov_math Time codes: 00:00 Greeting and connection check 01:07 Getting to know the teacher 01:54 Intensive course topic 02:36 Where the classes will be held intensive 03:04 Intensive course plan 03:19 About task 14 of the profile Unified State Exam 04:05 Who is the intensive course intended for 06:10 Methods for solving problems in stereometry 06:37 Stay in touch 07:02 Intensive course dates 07:33 Answers to questions 09:14 What is a coordinate system 11:58 Vector and its characteristics 13:50 Who needs the second part of stereometry 14:41 Vector coordinates 16:17 Problem 1 - vector coordinates 18:33 Answers to questions on problem 1 19:48 Sum and difference of vectors 20:28 Problems 2 and 3 - sum and difference of vectors 23:14 Graphical representation of the sum and difference of vectors 25:30 Answers to questions on problems 2 and 3 26:14 Vector length 28:15 Dot product of vectors 31:39 Problem 4 - the scalar product of vectors 31:58 Problem 5 - the angle between vectors 33:39 Answers to questions on problems 4 and 5 37:40 Proof of the formulas for the scalar product of vectors 43:28 Problem 6 - the equation of a line 47:51 Answers to questions on problem 6 50:49 Problem 7 - a point and a plane 53:40 Problem 8 - the equation of a plane 59:54 Restart of the annual course 1:00:37 Beefsteak Course 1:01:21 Course Features 1:02:51 Promo Code for Purchasing the Course 1:06:14 Answers to questions on problem 8 1:09:38 Problem 9 - Proof of Perpendicularity of Lines 1:17:33 Answers to questions on problem 9 1:22:39 Problem 10 - Proof passing a straight line through a point 1:35:48 Answers to questions on problem 10 1:40:38 Problem 11 - proof of the ratio of segments 1:57:22 Answers to questions and summing up the lesson #eg2024 #stereometry #mathematics
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