The combination of several centers of triangle and vector in senior one If we know that O is a point in the plane of the triangle and satisfy the following conditions: module of vector OA + module of BC = module of OB + module of Ca = module of OC + module of AB, then what center of the triangle is o?

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• 1. The known vector a = (COS α, sin α) B = (COS β, sin β), |a-b | = 5 / 5 under 2 roots Find the value of COS (α - β)
• 2. What do you mean by collinear and noncollinear in vector addition and subtraction!
• 3. It is known that m.n is the midpoint of vector AB and vector CD of any two line segments, and the vector Mn = 1 / 2 (vector AD + vector BC) is proved
• 4. It's almost the first semester of senior high school. We need to learn compulsory five in Mathematics: solving triangles, sequence of numbers and inequality. How much do these have to do with compulsory one?
• 5. High school mathematics vector inequality synthesis Given the vector a = (y, x + 5), B = (y, x + 5), x > 0, Y > 0, and a is perpendicular to B, what is the minimum value of XY Change a = (4-x, 1)
• 6. A problem of solving the combination of triangle and vector In the triangle ABC, h is perpendicular, the dot product of vector BH and vector BC is 6, the sum of squares of sina and sinc = the square of SINB + Sina * sinc Find: (1) angle B (2) When the radius of circumcircle r of triangle ABC is the smallest, the shape of triangle ABC can be judged
• 7. Solving triangle with vector In △ ABC, the opposite sides of angles a, B and C are a, B, C and Tanc = 3 times the root sign 7, so COSC can be obtained
• 8. Solve the combination of triangle and vector It is known that a, B and C are the opposite sides of three internal angles a, B and C of Δ ABC, vector m (radical 3, - 1) and vector n (COSA, Sina). If vector m, vector N and acosb + bcosa = csinc, then angle B =?)
• 9. Solving a big problem of triangle and vector in Mathematics Let a = (SiNx / 2, root 3cosx / 2) and B = (cosx / 2, cosx / 2). Let f (x) = a · B (1) Find the zero point of function f (x) on [0,2] () let the opposite sides of △ ABC inner angles a, B and C be a, B and C respectively, and f (a) = root 3 If you're not finished, add: B = 2, Sina = 2sinc, find the value of C
• 10. A minimalist fraction, expand its numerator by three times, reduce its denominator by two times, and it becomes 92. Can you find out what the original minimalist fraction is?
• 11. A mathematical problem about vector of grade one in Senior High School Given that the module of vector a is 3, B = (1,2), and a is parallel to B. find the coordinates of A Please write down the detailed process
• 12. Mathematical problems of triangle vector In the triangle ABC, the opposite sides of the angle ABC are ABC, vector M = (B + C, a), n = (a - √ 3C, B-C), if vector M / / N, 1. Find the size of angle B 2. The value of COS (B + 10 °) × [1 + √ 3tan (b-20 °)]
• 13. A mathematical problem about vector in senior one Given a (1,0), line L: y = 2x-6, point R is a point on line L, if RA vector = 2AP vector, find the trajectory equation of point P
• 14. Mathematical problems about vectors In △ ABC, satisfy: ab ⊥ AC, M is the midpoint of BC (1) If | ab | = | AC |, find the cosine of the angle between vector AB + 2Ac and vector 2Ab + AC; (2) If O is any point on the line am, and | ab | = | AC |, = root 2, find the minimum value of OA * ob + OC * OA (3) If P is a point on BC, and AP = 2, AP * AC = 2AP * AB = 2, find the minimum value of | AB + AC + AP |
• 15. Ask a math problem about vectors and triangles? O is always a point in the triangle ABC, and there are: OA ^ 2 + BC ^ 2 = ob ^ 2 + Ca ^ 2 = OC ^ 2 + AB ^ 2, proving: ab ⊥ OC. Note: in the condition, OA, BC, ob, CA, OC, AB are the form of module length of vector; in proving, AB and OC are the form of vector
• 16. Prove three high intersection of triangle and one point
• 17. In the straight triangular prism abc-a1b1c1, Aa1 = BC = AB = 2, AB is perpendicular to BC, find the size of dihedral angle b1-a1c-c1, which two planes are b1-a1c-c1? Just type a word. I already know it, No one wants points
• 18. As shown in the figure, BD and CE are the heights of △ ABC, and BD = CE
• 19. In the straight triangular prism abc-a1b1c1, if ∠ BAC = 90 ° AB = AC = Aa1, then the angle between the out of plane straight line BA1 and AC1 is equal to () A. 30°B. 45°C. 60°D. 90°
• 20. It is known that, as shown in the figure, in △ ABC, the bisector of ∠ ABC and ∠ ACB intersects at point o