The definition of finding the inner product of two vectors 3Q It's on the first floor. Where is it? Inside and outside the points. Do you belong to the inside? What about the outside? Can you tell me? In addition, I'm talking about vectors in linear algebra.

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• 1. On a vector product of quantity Given the vector a + vector B + vector C = 0 vector, and the module of a vector = 4, the module of B vector = 3, the module of C vector = 5 Finding a vector x C vector
• 2. On the scalar product of several vectors (1) |a | = 2, B = (- 2,4), and a ⊥ B, then a coordinate of a is_______ (2) Given a = (5,8), B = (2,3), C = (1, - 2), then (a * b) * C=___________ (3) Given that | a | = 8, a * b = - 12, then the number of projections of B in a direction is_____________
• 3. Vector product of higher numbers There are three vectors a, B, C, and their modules are known. When the sum of these three vectors equals to zero vector, the A × B + B × C + C × a, where a × B, B × C, C × a are their vector products
• 4. In high numbers: what is the relationship between arcsinx and SiNx What is the relationship between arcsinx and SiNx What about arccosx
• 5. Arctanx ^ 2 / (SiNx / 2) * SiNx
• 6. High number: limx - π / 2 (2sinx ^ 2-sinx-1) / (SiNx ^ 2 + sinx-2) limit
• 7. Can you imagine the size of 100 million It is said that king sherhan wanted to reward the inventor of chess, the prime minister Dayer. Dayer pointed to the chess board and said, "Your Majesty, please give me one grain of wheat in the first small space of the board, two grains of wheat in the second small space, and four grains of wheat in the third small space. Go on like this, The wheat in each small grid is twice as much as that in the previous one. Then give all the 64 grids of wheat on the chessboard to your servant! "The king ordered his servant to put a bag of wheat in front of the chessboard, but the bag was empty before it was put into the 20th grid. So the wheat was carried in bag by bag, and the warehouse was empty, The checkerboard has not put all the grains of wheat on it. King sherhan thought that he had been cheated If you put the wheat in the () grid, it will have more than 100 million grains; if you put the wheat in the 64th grid, it will have about 100 million grains
• 8. In the market, hawkers are often heard shouting: "a 10 yuan toy racing car is 20% off. Come and buy it quickly." "can it be two or two yuan cheaper?" Xiao Ming asked. If the hawker sells it for two yuan, he can still make a profit of 20%. According to the formula (purchase price x profit rate = sales price x discount number - yield number - purchase price), how much is the purchase price of a toy racing car?
• 9. If a commodity is sold at a 10% discount on the price, it will make a profit of 25 yuan. If it is sold at a 20% discount on the price, it will lose 20 yuan. How much is the purchase price of the commodity
• 10. Divide 2008 into the sum of n natural numbers, and the digits of these n natural numbers are the same. If you erase all the digits of these n natural numbers, the remaining array will become an arithmetic sequence with tolerance of 6. The maximum of n is______ ．
• 11. What is the inner product of a vector? What's the use?
• 12. The definition and basic properties of vector inner product, 1. Given vector a = (1, radical 3), vector b = (- radical 3, - 1), find 2. Given points a (x, - 1), B (- 2, - 6), C (1, - 2) and | vector ab | = | vector AC |, find the value of X 3. Given points a (x, 4), B (2, y + 3), and vector AB = (3, 6), find the value of X, y
• 13. On the inner product of vector How did the vector inner product formula come from? What's the reason for the inventor to stipulate that, and the vector multiplied by the vector is a constant
• 14. What does the square of vector a represent? What is the geometric meaning? Such as the title
• 15. What is the outer product of a vector, what is its geometric and arithmetic significance, and how to find it?
• 16. Given the vector | a | = 4 and the vector | B | = 3, the scalar product is obtained under the following conditions: 1 / vector a is perpendicular to vector B 2 / the angle between vector a and vector B is 60 ° 3 / vector a is parallel to B
• 17. The scalar product problem of the first higher vector: we know that the vector a = (1 + √ 3), the angle between B and a is 3 / π, and a * b = 4 It is known that the vector a = (1 + √ 3), the angle between B and a is 3 / π, and a * b = 4 (1) Find the vector B; (2) Let m = a + KB, n = 3ka-2b (k is a positive real number). When m ⊥ n, whether M + N and a are collinear or not is the reason
• 18. If the vector a = (0,3) and the vector b = (- 4,4), then the scalar product of the vectors a and B is?
• 19. To find the coordinate vector, vertical and parallel calculation formula
• 20. How to memorize the formula of the vertical and parallel coordinates of two vectors?