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Afiinseks ruumiks. Tasandi võrrandid. 1. Tasand läbib punkte A(2; -1; 5) B(3; 0; 7) C(6; -4; 12). Kirjutada tasandivõrrand. Toome sisse muutuva punkti P(x; y; z). AB = (1; 1; 2) AC = (4; -3; 7) AP = ( x -2; y + 1; z 5) AP = AB + AC Tasandi võrrand determinant kujul: 1 1 2 4 -3 7= 0 x -2 y+1 z- 5 Tasandi üldvõrrand: 13x + y 7z 10 = 0 2. Tasand läbib punkti P0( -3; 4; 5) ja normaalvektor on n = (2; -6; 7). Leia tasandi üldvõrrand. (toon sisse muutuva punkti P( x; y; z) P0P n = 0 P0P = (x +3; y -4; z 5) Ax + By + Cz + D = 0 n = (A; B; C) 2 ( x +3) -6 (y 4) + 7 (z 5) = 0 2x + 6 -6y +24 +7z 35 = 0 2x - 6y +7z -5 = 0 3. Tasand läbib punkti P0(6; 0; 8) ja rihivektorid on u = (3; -1; 4) ja v = (2; 5; -7). Toon sisse muutuva punkti P (x; y; z).
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4. -1 2.5. b3 2.6. 0 2.7. cos 2 2.8. 2tan - 20 - Lineaaralgebra elemendid. M.Latõnina 2.9. 68 2.10. 258 2.11. -26 2.12. -119 2.13. 4 2.14. 8 2.15. 14x + 5y 7z + 23 2.16. 2 (ad bc) 2.17. 2 (x3 y3 ) 2.18. A3 3 ABC + B3 + C3 11 2.19.1. x1 = 2; x2 = 3 2.19.2. x1 = 2; x2 = - 2.20. 81 7 2.21. 0 2.22. -32 2.23. -246 2.24. 8 2.25. 93 2.26. -393 2.27. 12 2.28. -843 2.29
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