векторы 11 класс

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    16-Jun-2015

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  • 1. 10 179 : ..

2. , . , . 3. D F 4. 1 : (x1, y1, z1); B (x2, y2, z2). . 5. 2 : m {m1, m2, m3}; n {n1, n2, n3}. : ) ; ) . 6. 3 a b, , {xa, ya, za}; b {xb, yb, zb}. 7. 1. () = k 2. D - B = D BC = AD 8. 3. m : k OC = OA + OB k + m k k + m m k = m CB k > 0 m > 0 9. 4. A = A2 1 A = = (A + )2 1 5. , , = A + ( ), + = 1 10. 6. , , D = A + + ( ()), + + = 1 7. M MA + MB + MC = 0 M = (A + + OC)3 1 11. A D 1 5 D1 = DA 2 5 D1 = DB 3 5 D1 = DC 4 1 11 1 DM ? DM1 12. DM1 = xDM DM = (DA + DB + DC) 3 1 1) DM ? DM1 2) , M ABC? 13. 3) : ) DA D1? ) DB DB1? ) DC DC1? 2 DA = DA1 5 3 DB = DB1 5 DC = DC1 4 5 14. 4) (2) (3) (1): DM1 = DA1 + DB1 + DC1 6 5x 9 5x 12 5x 15. 5) ? + + = 1 6 5x 9 5x 12 5x x = 65 36 : 36 : 65. 16. 2 A D F N M L K 17. 2 1) , KLMN ? KN = ML KN = ON OK 2) KN N K? 18. 2 3) , N BF? ON = (OB + OF) 2 1 4) , OF = (OC + OD) 2 1 OE = (OA + OB) 2 1 F D, E . 19. 5) KN, KN = (OB OC + OD OA) 4 1 7) . 6) MN. KNLM . ML = (OD OA + OB OC) 4 1 20. 3 : 2 361)( xxxxf += 21. a 3 2 231)( xxxxf += { } { }3;1 2;1 2 b xxxa 3. .b 4. ? ba 6. . 5. ? ba 2. .a b b 1. .)( fD 22. 4 D K, M, N CD, AD, AB . ABC. MO KN. 23. 4 A D O N a b M K 24. a b a b 1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 25. 3. D. 2. ( D). 10. os . 11. . 1. MO ( D). 5. KN DN DK. 6. N AB. 7. K DC. 9. : ) MO KN, ) MO, ) KN. 4. a, b, c. 8. KN a, b, c. 26. !