Random problems from the Unified State Exam.

[ComanderZhabikKlavik 5,619]

Hi everypony! Here I will publish random problems from the Unified State Exam in specialized mathematics, for which I am preparing, and their solutions in a spoiler.

All types of problems on the Unified State Exam:

1. Planimetry
2. Vectors
3. Stereometry
4. Elements of Probability Theory
5. Probabilities of Complex Events
6. Simple Equations
7. Calculations and Transformations
8. Derivative and Antiderivative
9. Problems with Applied Content
10. Text Problems
11. Graphs of Functions
12. Largest and Smallest Values of Functions
13. Equations
14. Stereometry Problem
15. Inequalities
16. Financial Mathematics
17. Planimetry Problem
18. Problem with a Parameter
19. Numbers and Their Properties

 

Problem 2. Vectors.

This math problem is taken from the website: https://math-ege.sdamgia.ru/problem?id=644849

Vectors  and  are depicted on the coordinate plane. Find the scalar product of a multiplied by .

 

Solution to this problem:

Spoiler