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Must a directed line segment be a vector?
Not necessarily! For example, if a vector calculates the inner product, your directed line segment can't calculate the inner product. Only sometimes we don't calculate the inner product, we can express a vector as a directed line segment
In addition, don't worry, this kind of question ~ entrance examination, college entrance examination papers will not be involved, will avoid fuzzy situation
A vector has only two elements: direction and size
The directed line segment has three elements: starting point, direction and size
We often use directed line segments to represent vectors. Vectors can be represented by one lowercase letter or two uppercase letters, that is, the starting point and the ending point of a line segment. Drawing a graph is a directed line segment. You can express it like this: vectors can be represented by directed line segments
Vectors are free and can be translated. Different directed line segments can be equal vectors. Vectors can have addition, subtraction, number multiplication, or inner product or outer product operations, but directed line segments cannot
The vectors before and after translation are equal, but the directed line segments are different
How can a vector be a directed line segment with coordinates
Take the coordinate origin as the starting point, then according to the direction, the distance to determine that point is the vector coordinates
Of course, if we take (1,1) as the starting point and (3,4) as the ending point, the vector coordinates are (2,3)
A directed line segment is a vector, and a vector is a directed line segment, right? Why
The two cannot be confused at all
Vector has the properties of dot product, projection, translation, addition and subtraction, while directed line segment has none of these properties!
The inverse of a directed line segment can have its unit direction vector
If two vectors are not equal, can they be represented by the same directed line segment
If two vectors are not equal, they must not be represented by the same directed line segment
The answer is yes. A vector itself is a directed line segment. Since two vectors are not equal, they cannot be represented by the same directed line segment, but they may be on the same line
RELATED INFORMATIONS
- 1. If two non-zero vectors can not be represented by the same directed line segment, then the two vectors are not equal and the proposition is true Among the three elements of a directed line segment, there are starting points. The starting points are different, and the directed line segments are different. The vector has nothing to do with the starting point, but only the size direction. So it should be a false proposition, but it will be dead. In the fourth assignment, it is said that this is a true proposition,
- 2. F (x) = cosx √ ((1-sinx) / (1 + SiNx)) + SiNx √ ((1-cosx) / (1 + cosx)) to find monotone intervals and ranges on f (π / 4) and (π / 2, π) F (x) = cosx √ ((1-sinx) / (1 + SiNx)) + SiNx √ ((1-cosx) / (1 + cosx)) 1, find f (π / 4) 2, find the monotone interval and range of function on (π / 2, π)
- 3. Why does limx / 1-cosx = infinity instead of equal to 1?
- 4. Limx → x power of 0 e - x power of - E / X
- 5. Limx tends to 0 [(1 / x) - (1 / SiNx)]
- 6. If three different prime numbers m, N, P satisfy m + n = P, then the minimum value of MNP is______ ．
- 7. M and N are prime numbers, and the square of 96 + n is equal to the square of m to find m and n
- 8. If a four digit number is the product of three primes and the sum of the squares of the three primes is 39630, then the natural number is?
- 9. I and the other number are prime numbers. Our sum is 19. Who are these two numbers?
- 10. There are two prime numbers, the sum of which is an odd number less than 100 and a multiple of 17. Find these two prime numbers
- 11. As shown in the figure, in △ ABC, ad ⊥ BC, CE ⊥ AB, perpendicular feet are D and e respectively, ab = 6, ad = 5, BC = 4 are known, and the length of CE is calculated
- 12. In △ ABC, ab = Acad is perpendicular to BC, the perpendicular foot is D, an is the bisector of ∠ cam, CE ⊥ an, the perpendicular foot is e When △ ABC satisfies what conditions, the quadrilateral adce is a square
- 13. As shown in the figure, ab ‖ CD, BC ⊥ AB, if AB = 4cm, s △ ABC = 12cm2, find the height of AB edge in △ abd
- 14. If ABC = 1, then the value of AAB + A + 1 + BBC + B + 1 + CCA + C + 1 is () A. 1B. 0C. -1D. -2
- 15. Given a + B + C = 0, the value of the algebraic formula (a + b) (B + C) (c + a) + ABC is () A. -1B. 1C. 0D. 2
- 16. It is known that a, B and C are the three sides of △ ABC, and the value of a, B and C is such that the value of fraction (AB AC + the square BC of C) A-B is 0. Judge the shape of the triangle and explain the reason
- 17. If the three sides of △ ABC satisfy a2-2bc = c2-2ab, then △ ABC is () A. Isosceles triangle B. right triangle C. equilateral triangle D. acute triangle
- 18. If a and B are real numbers and 1 / A-1 / b = 1 / (a + b), then the values of B / A-A / b are? A, - 1 B, 0 C, 1 / 2 D, 1 A、-1 B、0 C、1/2 D、1
- 19. When a is what kind of real number, the following formula has meaning in the range of real number: (1) a + 2 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (2) 3 − a
- 20. If the opposite number of a number is non positive, then the number must be: A, positive B, non positive C, non negative D, negative