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

OA ^ 2 + BC ^ 2 = ob ^ 2 + Ca ^ 2 = OC ^ 2 + AB ^ 2oa ^ 2-ob ^ 2 = Ca ^ 2-bc ^ 2 (OA + OB) (oa-ob) = (Ca + CB) (ca-cb) BA (OA + OB) - BA (Ca + CB) = 0ba (OA + ob + AC + BC) = 0ba (OC + OC) = 0ab · 2oC = 0ab · OC = 0

RELATED INFORMATIONS

1. 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 |
2. 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
3. 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 °)]
4. 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
5. 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?
6. 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)
7. What do you mean by collinear and noncollinear in vector addition and subtraction!
8. 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
9. 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?
10. 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)
11. Prove three high intersection of triangle and one point
12. 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
13. As shown in the figure, BD and CE are the heights of △ ABC, and BD = CE
14. 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°
15. It is known that, as shown in the figure, in △ ABC, the bisector of ∠ ABC and ∠ ACB intersects at point o
16. It is known that in △ ABC, ∠ a = 60 ° and the bisectors of ∠ ABC and ∠ ACB intersect at point O, then the degree of ∠ BOC is 0______ Degree
17. In the triangle ABC, where ∠ a = 40 ° and O is the intersection of the bisectors of ∠ ABC and ∠ ACB, then ∠ BOC=______ ．
18. In the triangle ABC, ∠ a = 80 degrees, the bisector of the outer angles of ∠ B and ∠ C intersects point O, and ∠ BOC?
19. It is known that the side edges of the triangular prism abc-a1b1c1 are equal to the sides of the bottom. The projection of A1 in the plane ABC is △ ABC It is known that the side edges and the bottom sides of the triangular prism abc-a1b1c1 are equal, and the projection of A1 in plane ABC is the center of △ ABC, then the sine value of the angle between Ab1 and plane ABC is △ ABC To process! Write a good reward to
20. It is known that the side edges and the bottom sides of the triangular prism abc-a1b1c1 are equal, and the projection D of A1 on the bottom ABC is the midpoint of BC, then the cosine value of the angle between AB and CC1 is? Trouble with space vector and solid geometry method to give solutions