What is the geometric meaning of the dot product of two vectors greater than zero?

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• 1. Why is the "product of vectors" the multiplication of modules of two vectors and then the multiplication of cos? Is this artificial? Or is there any basis?
• 2. Why does vector multiplication have negative numbers? This is a problem of coordinate multiplication Isn't vector multiplication length? How can there be negative numbers?
• 3. Is the coordinate point multiplication of vector the corresponding coordinate multiplication
• 4. What is the result of multiplication of vector coordinates? How did it become a number?
• 5. How to express the multiplication of two coordinate vectors?
• 6. 1. In equilateral triangle ABC, the angle between vector AB and vector BC is a.90 degree b.60 degree c.120 degree d.45 degree (why choose C). 2. In triangle ABC, if vector ab × vector BC > 0, then the triangle is? 3. Given that unit vectors E1 and E2 are perpendicular to each other, then (a + 2b) × (3a-b) =? 3 there is a mistake. It should be (3e1-2e2) × (E1 + E2) =?
• 7. In a regular triangular pyramid p-abc, if the three side edges are perpendicular to each other and the side edge length is a, then the distance from point P to plane ABC is () A. aB. 22aC. 33aD. 3a
• 8. Mathematics problems in senior two (space vector) Let a, B, C, d be four non coplanar points in space, and satisfy (vector AB) * (vector AC) = 0, (vector AB) * (vector AD) = 0, (vector AC) * (vector AD) = 0 Then triangle BCD is () triangle? A. Obtuse angle B. Right angle C. Acute angle D. Equilateral Why?
• 9. I don't quite understand the definition of sufficient condition and necessary condition. I've seen the definition many times, but I still can't understand it. Tell me about the following two questions· 1. For any real number a, B, C, the true proposition is (b) A. "Ab > BC" is the necessary condition of "a > b", and "AC = BC" is the necessary condition of "a = B" C. "AC > BC" is a sufficient condition for "a > b" and "AC = BC" is a sufficient condition for "a = B" 2. It is known that a and B are real numbers which are not equal to 0. What is the condition for "A / b > 1" to be "a > b"? And prove your conclusion
• 10. The perimeter of isosceles triangle is 2p, it revolves around the bottom to form a geometry. When we ask the length of each side of the triangle, the volume of the geometry is the largest?
• 11. What happens when two vectors that are not in the same plane are added or multiplied? (solid space)
• 12. What's the meaning of space vector multiplication? Why do two vectors multiplication give coordinates in the question? How to use coordinates?
• 13. What's the difference between the scalar product of a vector and the multiplication of two vectors? Generally speaking, what do two vectors OA · ob represent? For example, why is the multiplication of two vectors in the first question not equal to | OA · | ob | cos Sita?
• 14. What does vector multiplication equal to 1 mean?
• 15. It is proved that the intersection line of two planes is perpendicular to the plane formed by the normal vectors of two planes
• 16. Are the normal vectors of two planes perpendicular to each other and parallel to each other?
• 17. On vector and scalar Why are velocity and acceleration vectors? They don't use parallelogram rule when they are calculated, And they can also be compared in size How to distinguish between vector and scalar?
• 18. If the vector field F (m) is the gradient of a certain scalar function f (m), then it is called a potential function of F (m) f (m), and f (m) is called a potential field
• 19. Does the negative gradient direction refer to the opposite direction of the gradient direction? If it is a binary function, after the gradient is calculated, will it directly add a negative sign to the formed vector?
• 20. Is the gradient direction of a binary function unique at a point, or is there countless? Is it the normal direction of the point on the isoline?