![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Maths Senior One 》》》 The following lowercase letters are all vectors If the nonzero vector a, b satisfies |a+b|=|b|, then... ( ) (A)|2a|>|2a+b| (B)|2a||a+2b| (D)|2b|
Select the special value method:
Suppose a, b vector direction is opposite.|a|=2|b|=1
Bring in 4 options to select the qualified ones.
A. Definitely right. Just do it. Efficiency comes first.
Select the special value method:
Suppose a, b vector direction is opposite.|a|=2|b|=1
Bring in 4 options to select the qualified ones.
A. It's right. Just do it. Efficiency comes first.
Vector computation problem Given that the vector a, b satisfies (a+2b)×(a-b)=-6, and the module of a =1, the module of b =2, the angle between a and b is Given that triangle ABC is isosceles triangle, angle C=90°, AB=4, then vector AB×vector BC=
1|A|=1,|b|=2(a+2b)·(a-b)=|^2-2|b|^2+a·b=1-8+a·b=-6, i.e. a·b=1, i.e. cos=a·b/(|a b|)=1/2, i.e.=π/32BC projection on BA:|BC|cosB=2, i.e.|BC|=2/cosB=2/cos (π/4)=2√2, i.e. AB·BC=|AB BC|* cos (π-π/4)=4*2√2...
Space Vector and Its Application 1 In the known cuboid ABCD-A1B1C1D1, E and F are the points on A1D and B1D1, respectively, and A1E/A1D=B1F/B1D1.
Take K on D1D and make D1K/KD=A1E/ED, then EK//A1D1. Similarly, take a point T on D1C1 and make FT//B1C1, then EK//A1D1//B1C1//FT.EK/A1D1=DE/A1D=D1F/D1B1=FK/B1C1. Then A1D1=B1C1, then EK=FT, EKTF is parallelogram, EF//KT, KT is on C1CDD1, EF is not on C1CDD1.
Fast and skillful calculation 192192*368-368368*192
192*368*1001-368*1001*192=0
Fast and skillful calculation of sixth grade mathematical thinking training (1)73 Of 17 divided by 9(2)2222*1.7+3333*0.4+6666*0.9
(72+17/18)*1/9Th
1111*3.4+1111*1.2+1111*5.4
=1111*(3.4+1.2+5.4)
That's enough, right?
(72+17/18)*1/9
1111*3.4+1111*1.2+1111*5.4
=1111*(3.4+1.2+5.4)
All right?
The vector follows the parallelogram rule. So what is the parallelogram rule?
When two forces are combined, the line segment representing the two forces is used as a parallelogram, and the diagonal between the two adjacent sides represents the magnitude and direction of the resultant force, which is called parallelogram rule
RELATED INFORMATIONS
- 1. Do all vectors follow the parallelogram rule? Does the non-collinear force follow the parallelogram rule?
- 2. Verify which is the experimental value and which is the theoretical value in the parallelogram rule of force? Is the resultant force of F1, F2 or the force F of a force?
- 3. What is the law of the center of gravity of an ordinary triangle?
- 4. As shown in the figure, DE is the median line of the triangle ABC, and the median line theorem of the triangle is proved by the vector method
- 5. The vector proves that the three center lines of the triangle intersect at one point, 1. Prove that the three center lines of the triangle intersect at one point (all the following letters represent vectors) Let AC=a, BC=b as substrate AB=a-b, AD=a-(b/2), BE=(-a/2)+b Let AD and BE intersect at G1, and assume that AG1=λAD, BG1=μBE, Then AG1=λa-λb/2, BG=(-μa/2) b Since AG1= AB+BG1=(1-(μ/2)) a =(μ-1) b Therefore, the equation can be solved as follows:λ=μ=2/3, so AG1=2/3AD If AD and CF intersect at point G2, the same method can prove that AG2=2/3AD (How to prove here, do you have to reset the base? I can't solve it with the old base, or I' ve calculated what's wrong. Write down the steps summarized in the last "the same way ". Thank you)
- 6. CONDITIONS OF THREE POINT COLLINEARITY IN SPACE
- 7. What is the general way to prove three-point collinearity Don't use space vectors! Proving the Relation of Point, Line and Surface in Space What methods do we have to prove that three points are collinear Don't use space vectors! Proving the Relation of Point, Line and Surface in Space
- 8. A Proof of Plane Vector ~ Help Me ~ If vector a=(cosα, sinα), vector b=(cosβ, sinβ), then vector a and vector b must satisfy (a+b)⊥(a-b). Why...? Please describe the detailed process and ideas ~ Thank you so much~~! A Proof of Plane Vector If vector a=(cosα, sinα), vector b=(cosβ, sinβ), then vector a and vector b must satisfy (a+b)⊥(a-b). Why...? Please describe the detailed process and ideas ~ Thank you so much~~! A Proof of Plane Vector ~ Help me ~ If vector a=(cosα, sinα), vector b=(cosβ, sinβ), then vector a and vector b must satisfy (a+b)⊥(a-b). Why...? Please describe the detailed process and ideas ~ Thank you so much~~!
- 9. Calculation: (1)(3A^2-ab+7)-(-4a^2-2ab+7)(2)3xy-5xy-(-2xy) (3)(-X^2+5+4x)+(5x-4+2x^2), where x=-2
- 10. What methods can be used to reduce the calculation errors when drafting? Some people whisper numbers, but I don't like it (Ask a math expert) What can be done to reduce the computational errors when drafting? Some people whisper numbers, but I don't like it (Ask a math expert) What methods can be used to reduce calculation errors when drafting? Some people whisper numbers, but I don't like it
- 11. Right-hand spiral law?
- 12. Rational set: irrational set: positive real set: real set: As follows:-11, root 5,3, root 9/11,0,2/3, root 196,-π,0.4, root 2/3
- 13. I sold 1,450 yuan this morning, including 200 for shoes and 1,250 for clothes.
- 14. Two date periods are known in C #, For example, good days from December 1,2008 to January 4,2009?
- 15. A Simple Mathematical Calculation 20/9/8/11/9/2X11/8
- 16. Add, subtract, multiply and divide by (2,5,5,9,9) to obtain 95. There can be fractions, decimals.
- 17. How's my math, okay? I was in Rainbow Middle School, September 2014. We formally took the math test 13 times, each time the full score is 120 points, my grades are (unit: points):114,112,116,117,113,117,120,120,108,109,120,120,115. The average grade is usually 80.
- 18. What is the number of e in mathematics? How did you figure it out?
- 19. Commonly used vector formulas for electromagnetic field interpretation Why does this formula have both A gradient and A divergence? I think only scalar can find gradient, only vector can find divergence. So why can this A be found?
- 20. Take a certain direction as the positive direction. If F=-5N, it indicates that the force is 5 N, and the direction is opposite to the positive direction. If F=5N, it indicates that the force is 5 N, and the direction is the same as the positive direction; or only the force is 5 N, and the direction is unknown. If F=5N, how to distinguish the two cases! Judge the right and wrong of the phrase "sometimes the direction of a vector is represented by a positive and negative sign, the purpose of which is to simplify vector operations on the same line into algebraic operations "!