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How to use the knowledge of vector to prove the intersection of with the Knowledge of Vector How to Prove the Intersection of Triangular Centerlines with the Knowledge of Vector
Let the midpoint of BC be D midpoint be E, AD intersect BE at O, connect CO extension intersect AB at F vector AD=1/2(AC+AB) OD=1/3AD=1/6(AC+AB)=1/6(AC+CB-CA) CO=CD+DO=1/2CB+1/6CA-1/6CB+1/6CA=1/3(CB+CA) Set vector CB+CA=CG, connect GA, GB, GC, and CG intersect AB at F ́.
Using Vector Method to Prove the Intersection of Triangular Divide Lines at One Point
In △ABC, AD, BE, CF are the bisectors of ∠A,∠B,∠C, respectively.
To prove that the vertical bisectors of three sides of a triangle intersect at one point by a vector Verifying that the vertical bisector of three sides of a triangle intersects at a point by means of a vector
It is known that: BC⊥AH, AC⊥BH prove: AB⊥CH prove: because BC⊥AH, AC⊥BH so: vector BC·vector AH=vector AC·vector BH=0 so: vector BC·(vector AC+vector CH)=vector AC·(vector BC+vector CH)=0 so: vector BC·vector AC=-vector BC·vector CH=-vector AC·vector CH...
What is the three-point collinear condition? Expressed in a formula! And how?
P1(x1, y1), P2(x2, y2) and P3(x3, y3) are collinear:(y2-y1)/(x2-x1)=(y3-y1)/(x3-x1)– This is a necessary and sufficient condition, and is derived as follows:(y2-y1)/(x2-x1)=(y3-y2)/(x3-x2) or (y1-y2)/(x1-x2)=(y3-y2)/(x3-x2)– I don' t know what "how to use" is.
2.3 Quantity product of plane vector 1. Given vectors a, b satisfy |a|=3,|b|=2,|a+b|=4, then |a-b|=_____. 2. Given that |a|=|b|=1, the angle between a and b is 90 degrees, c=2a+3b, d=Ka-4b, c is perpendicular to d, then the value of K is _____. 3. Given |a|=|b|=|a-b|=1, then |a+b|=_______.
1.(|A+b|)^2=a^2+b^2+2*a*bcosC=9+4+2*abcosC=162abcosC=3(|a-b|)^2=a^2+b^2+2*a*bcosC=9+4-2*abcosC=102.c.d=(2a+3b).(Ka-4b)=2Ka^2-8a.b+3Ka.b-12b^2a.b=0c.d=2Ka^2-12b^2=2K-12=0K=63.|a-b|^2=a^2+b^2-2abcosC=1 ...
High School Mathematics Compulsory Four Plane Vector If two plane vectors in coordinate system are parallel, what formula is there, or what formula or method is there to prove that two vectors are parallel
How about x1*y2-x2*y1=0? Satisfied No
How about x1*y2-x2*y1=0? Satisfied?
RELATED INFORMATIONS
- 1. 1) Vector a, vector b satisfies |vector a|,|vector b|=10, then what is the value range of |vector a-vector b| 2) Given |vector a|=6,|vector b|=8,|vector a-vector b|=10, then |vector a+vector b| equals what 3) Given △ABC vertex A (-1,-1/2), B (2,3) and center of gravity coordinate G (1,1/2), what is the coordinate of vertex C? 4) Given the two points 0(0,0) and A (6,3), if point P is on the straight line OA, vector PA=2 vector OP, and P is the midpoint of line OB, what is the coordinate of point B? 5) Given vector a=(1,2) vector b=0(1,1) and the angle between vector a and vector a +β vector b is acute, what is the value range of real number β?
- 2. Collinear problem of plane vector Let vector AB=√2/2×(a+5b), vector BC=-2a+8b, vector CD=3*(a-b), then the three points of collinear are
- 3. A point O in triangle ABC proves that vector OA+vector OB+vector OC is equal to vector 0.
- 4. In triangle ABC vector A B =4 vector AC =2 vector AD =1/3 vector AB +2/3 vector AC proves BCD three points collinear when vector AD = root 6 find vector BC In triangle ABC vector A B =4 vector AC =2 vector AD =1/3 vector AB +2/3 vector AC proves BCD three point collinear when vector AD = root 6 find vector BC
- 5. In the concept of the product of must the vector be non-zero? In the concept of the product of the vector must be non-zero?
- 6. Given the rectangle ABCD-A' B' C' D', simplify the following vector expressions and mark out the vector of the simplified result. {1} Small arrow above AB + small arrow above BB'; {2} AB plus small arrow + BC plus small arrow + BB' plus small arrow. Given the rectangle ABCD-A' B' C' D', the following vector expression is simplified and the vector of the simplified result is marked. {1} Small arrow above AB + small arrow above BB'; {2} AB plus small arrow + BC plus small arrow + BB' plus small arrow.
- 7. Excuse me. A (5,1). B (7,10). Vector AB (how to calculate? , Answer is (2,9)
- 8. In ΔABC, D, E and F are the midpoint of AB, BC and CA respectively. BF and CD intersect at point O. Let vector AB=a and vector AC=b. Prove that AOE three points are on the same straight line, and AO: OE=BO: OF=CO: OD=2 Supplement to question: the answer is AE =1/2(a+b), so AO =(2/3) AE AO =(2/3) AE, how is this obtained?
- 9. Given three points A (-2,0,2), B (-1,1,2), C (-3,0,4), let a=AB, b=AC (1), find the angle between vector a and vector b.(2) If... A (-2,0,2), B (-1,1,2), C (-3,0,4) Let a=AB, b=AC (1) Find the angle between vector a and vector b.(2) If vector ka+b and vector ka-2b are perpendicular to each other, find the value of k.
- 10. Vector a, vector b is nonzero, if |vector a+vector b|=|vector a-vector b|, then the angle between vector a and vector b is?
- 11. The Method of Calculating the Distance from the Vertex to the Line by Using the Vector A Method of Calculating the Distance from the Point to the Line by Vector Proof
- 12. Is the collinear vector a parallel vector
- 13. Given O, A, B are three points on the plane,2 times vector AC + vector CB=0, find vector OC Given that O, A, B are three points on the plane,2 times vector AC + vector CB=0, find vector OC
- 14. If vector a, b is a nonzero vector, then vector a=— vector b is the ___ condition that vector a is parallel to vector b Why? If vector a, b is a nonzero vector, then vector a=— vector b is ___ condition of vector a parallel to vector b Why? Why?
- 15. Is the zero vector perpendicular to any vector? RT
- 16. Given Space Three Points A (0 2 3) B (-2 1 6) C (1-1 5) Find the area of parallelogram with ABAC as the side Using the Angle and Distance Formula to Do the Course There is also a case where vector a = root 3 and a is perpendicular to ABAC for coordinates of a Given Space Three Points A (0 2 3) B (-2 1 6) C (1-1 5) Find the area of parallelogram with ABAC as the side Using Angle and Distance Formula to Do the Course There is also a case where vector a = root 3 and a is perpendicular to ABAC for coordinates of a Given Space Three Points A (0 2 3) B (-2 1 6) C (1-1 5) Find the area of parallelogram with ABAC as the side Using the Angle and Distance Formula to Do the Course There is also a case where the vector a = root 3 and a is perpendicular to ABAC for the coordinates of a
- 17. What does the scalar product and vector product mean? Thank you, God.
- 18. How to calculate the vector |a+b|
- 19. How to calculate the resultant force by parallelogram rule?
- 20. What is the condition for three vectors to be coplanar?