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In the triangle, how to prove the "five-center" point with a vector? I'm talking about how each of them can prove it. For example, how to prove that the vertical center is the intersection of three high lines, only one. How do we prove the "five-center" intersection in a triangle with a vector? I'm talking about how each of them can prove it. For example, how to prove that the vertical center is the intersection of three high lines, only one. In the triangle, how to prove the "five hearts" with a vector? I'm talking about how each of them can prove it. For example, how to prove that the vertical center is the intersection of three high lines, only one.
For the triangle of the five-centered meaning, the heart, the heart, the heart and the heart, they should be five points! The center of gravity is the point of intersection of three high lines, only one. The center of gravity is the point of intersection of three angle bisectors, only one. The center of gravity is the point of intersection of three midlines, only one. The center of gravity is the point of intersection of three midlines, only one.
For the triangle of the five-centered meaning of the center of gravity, the heart, the heart, the heart and the heart, they should be five points! The center of gravity is the point of intersection of three high lines, only one. The center of gravity is the point of intersection of three angle bisectors, only one. The center of gravity is the point of intersection of three midlines, only one. The center of gravity is the point of intersection of three midlines, only one.
Vector Representation of Triangular Four Centers
0
How the inner is represented in the vector
Given that O is the inner part of the triangle ABC, a, b, c are the length of the opposite sides of A. B. C. Then aOA+bOB+cOC=0(OA, OB, OC all directives). It is proved that if the triangle ABC, AD is the angle bisector of BC, the inner part is O.|BC|=a,|AC|=b,|AB|=caOA+bOB+cOC=aOA+b (AB+OA)+c (AC+OA)=(a+b+c) OA+b (DB-...
The problem of combining the inner triangle with the vector. Let I be the inner value of the triangle ABC, AB=AC=5, BC=6, vector AI=m (multiple) vector AB+n (multiple) vector BC, the sum value. Let I be the inner of the triangle ABC, AB=AC=5, BC=6, vector AI=m (multiple) vector AB+n (multiple) vector BC, and find the value of M and N. The problem of combining inner triangle with vector. Let I be the inner value of the triangle ABC, AB=AC=5, BC=6, vector AI=m (multiple) vector AB+n (multiple) vector BC, and sum the values. Let I be the inner of the triangle ABC, AB=AC=5, BC=6, vector AI=m (multiple) vector AB+n (multiple) vector BC, find the value of M and N. The problem of combining inner triangle with vector. Let I be the inner value of the triangle ABC, AB=AC=5, BC=6, vector AI=m (multiple) vector AB+n (multiple) vector BC, the sum value. Let I be the inner of the triangle ABC, AB=AC=5, BC=6, vector AI=m (multiple) vector AB+n (multiple) vector BC, find the value of M and N.
DI is parallel to BC through point I, and intersects AB at point D. Connect AI and extend BC to E'm vector AB+n vector BC', i.e.'vector AD+vector DI'. Because DI is parallel to BC, AD is parallel to AB, so M*vector AB=vector AD N*vector BC=vector DI It is easy to know the radius of tangent circle of triangle 1.5, so EI=1.5 is known by similarity AD=25/...
Please use the vector method to prove that the three center lines of any triangle are coincident. Please use the vector method to prove that any triangle three - line point.
Let the triangle be ABC and the three center lines be AD, BE and CF, then the vector AD=1/2*(vector AC+vector AB), the vector BE=1/2*(vector BA+vector BC), the vector CF=1/2*(vector CA+vector CB).
Given the vector a=(sinx,3/2), b=(cosx,-1). When a is parallel to b, find the square of 2cosx-sin2x
Sinx*(-1)=3/2*cosx
Sinx/cosx=-3/2
Tanx=-3/2
2(Cosx)^2-sin 2x
= Cos2x+1-sin2x
=[1-(Tanx)^2]/[1+(tanx)^2]-2(tanx)/[1+(tanx)^2]+1
=[1-(Tanx)^2-2(tanx)]/[1+(tanx)^2]+1
=[1-9/4+3]/[1+9/4]+1
=16/13
RELATED INFORMATIONS
- 1. Given the vector a=(sinx- cosx,2cosx), b=(sinx+cosx, sinx).(1) if a⊥b, find the value of tan2x if a*b=3/5, find the value of sin4x The vectors a=(sinx- cosx,2cosx), b=(sinx+cosx, sinx) are known. (1) If a⊥b, find the value of tan2x 2 If a*b=3/5, find the value of sin4x
- 2. Given vectors a=(1,2), b=(2,-1), then the angle between vector a and vector b
- 3. Given vector a=(2,3), vector b=(-1,-2), vector c=(2,1), then (b•C) a=?
- 4. Given vector a=(-1, y) vector b=(1,-3) and satisfy (2a+b)⊥b 1. Find the coordinates of vector a 2. Find the angle between vectors a and b Vector a=(-1, y) vector b=(1,-3) and satisfies (2a+b)⊥b 1. Find the coordinates of vector a 2. Find the angle between vectors a and b
- 5. If the vectors a, b, c satisfy a+b+c=0, and /a/=3,/b/=1,/c/=4, then how much is a*b+b*c+c*a? Because /a/+/b/=/c/, and because a+b+c=0, a and b must be in the same direction direction, and c in the opposite direction. So a*b+b*c+c*a=/a//b/-/b//c/-/a//c/=3-4-12=-13 Find the reason why a and b must be in the same direction and c must be in the opposite direction. ——
- 6. Three vertices A (0,2), B (-1,-2), C (3,1) of a quadrilateral ABCD are known, and BC =2 AD, the coordinates of vertex D are () A.(2,7 2) B.(2,−1 2) C.(3,2) D.(1,3) Three vertices A (0,2), B (-1,-2), C (3,1) of the quadrilateral ABCD are known, and BC =2 AD, the coordinates of vertex D are () A.(2,7 2) B.(2,−1 2) C.(3,2) D.(1,3)
- 7. Given the vector a=(1,1), b=(4, x), u=a+2b, v=2a+b, and u is parallel to v, then x=
- 8. Given that the module of a vector is equal to 1, the module of b vector is equal to 2, find (a vector+2b vector)(2a vector-b vector)
- 9. Given the plane vector a, b,|a|=1,|b|=2, a perpendicular a-2b, then what is the value of |2a+b|
- 10. Given the vector a=(3,-1), b=(-1,2), then the coordinate of -3a --2b is? Just the results. Thank you.
- 11. Combining vectors to solve triangles In △ABC, the opposite sides of angles A, B and C are a,b,c,tanC =3 times the root number 7, and cosC is obtained Combining vectors to solve triangles In △ABC, the opposite sides of angles A, B and C are a,b,c,tanC =3 times the root number 7, and cosC is obtained.
- 12. What is the difference between quantity product and vector product? Does it matter?
- 13. What is the geometric meaning of the product of the number of vectors? If there is any physical knowledge involved, please speak in plain English. What is the geometric meaning of the product of the number of vectors? If physical knowledge is involved, please speak in plain English.
- 14. If the vector a=(1,-2),|b|=4|a|, and a, b are collinear, then the possible coordinates of b are If the vector a=(1,-2),|b|=4|a|, and a, b are collinear, then the possible coordinates of b are (-4,8)
- 15. Given non-zero vectors a, b and a perpendicular to b, verify that (absolute value of vector a + absolute value of vector b)/(absolute value of vector a + b) is less than or equal to root 2
- 16. How to find the normal vector of a plane made of triangles?
- 17. Given vectors OA, OB, OC and trilateral a, b, c, I are the inner of a triangle, prove vector OI=(aOA+bOB+cOC)/(a+b+c) Given vectors OA, OB, OC and trilateral a, b, c, I are the inner of a triangle, prove that vector OI=(aOA+bOB+cOC)/(a+b+c)
- 18. Give a proof of the theorem of the relationship between the diagonal and the sides of a parallelogram (the sum of the squares of the two diagonals of a parallelogram is equal to the sum of the squares of its four sides)
- 19. It is proved that if vector a*b+b*c+c*a=0, then a, b, c are coplanar. What's the theorem, what's the definition, what's the idea
- 20. In this paper, the vector method is used to prove that the three center lines of the triangle ABC intersect at a point P and have a Vector OP=1/3(vector OA+vector OB+OC vector) Note: Vector method is required instead of coordinates In this paper, the vector method is used to prove that the three midlines of the triangle ABC intersect at point P Vector OP=1/3(vector OA+vector OB+OC vector) Note: Vector method is required instead of coordinates