Кто-нибудь!!! Ответьте!!!! Через точки М1 (-6,6,-5) и М2 (12, -6,1) провели прямую. Найти точки пересечения этой прямой с координатными плоскостями.
Ответы
Ответ дал:
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прямая:
![frac{x+6}{12+6} = frac{y-6}{-6-6} = frac{z+5}{1+5} \ frac{x+6}{18} = frac{y-6}{-12} \ 3y-18=-2x-12\ 2x+3y-6=0\ frac{y-6}{-12} = frac{z+5}{6}\ y-6=-2z-10\ y+ 2z + 4 =0\ left { {{2x+3y-6=0} atop {y+ 2z + 4 =0}} right. frac{x+6}{12+6} = frac{y-6}{-6-6} = frac{z+5}{1+5} \ frac{x+6}{18} = frac{y-6}{-12} \ 3y-18=-2x-12\ 2x+3y-6=0\ frac{y-6}{-12} = frac{z+5}{6}\ y-6=-2z-10\ y+ 2z + 4 =0\ left { {{2x+3y-6=0} atop {y+ 2z + 4 =0}} right.](https://tex.z-dn.net/?f=+frac%7Bx%2B6%7D%7B12%2B6%7D+%3D+frac%7By-6%7D%7B-6-6%7D+%3D+frac%7Bz%2B5%7D%7B1%2B5%7D+%5C+frac%7Bx%2B6%7D%7B18%7D+%3D+frac%7By-6%7D%7B-12%7D+%5C+3y-18%3D-2x-12%5C+2x%2B3y-6%3D0%5C+frac%7By-6%7D%7B-12%7D+%3D+frac%7Bz%2B5%7D%7B6%7D%5C+y-6%3D-2z-10%5C+y%2B+2z+%2B+4+%3D0%5C+left+%7B+%7B%7B2x%2B3y-6%3D0%7D+atop+%7By%2B+2z+%2B+4+%3D0%7D%7D+right.+)
пересечение с Оху
![left[begin{array}{c} {2x+3y-6=0}\ {y+ 2z + 4 =0}\ {z=0}end{array}right\ left[begin{array}{c} {x=9}\ {y=-4}\ {z=0}end{array}right\ left[begin{array}{c} {2x+3y-6=0}\ {y+ 2z + 4 =0}\ {z=0}end{array}right\ left[begin{array}{c} {x=9}\ {y=-4}\ {z=0}end{array}right\](https://tex.z-dn.net/?f=+left%5Bbegin%7Barray%7D%7Bc%7D+%7B2x%2B3y-6%3D0%7D%5C+%7By%2B+2z+%2B+4+%3D0%7D%5C+%7Bz%3D0%7Dend%7Barray%7Dright%5C+left%5Bbegin%7Barray%7D%7Bc%7D+%7Bx%3D9%7D%5C+%7By%3D-4%7D%5C+%7Bz%3D0%7Dend%7Barray%7Dright%5C)
(9; -4; 0)
пересечение с Оуz:
![left[begin{array}{c} {2x+3y-6=0}\ {y+ 2z + 4 =0}\ {x=0}end{array}right\ left[begin{array}{c} {x=0}\ {y=2}\ {z=-3}end{array}right\ left[begin{array}{c} {2x+3y-6=0}\ {y+ 2z + 4 =0}\ {x=0}end{array}right\ left[begin{array}{c} {x=0}\ {y=2}\ {z=-3}end{array}right\](https://tex.z-dn.net/?f=+left%5Bbegin%7Barray%7D%7Bc%7D+%7B2x%2B3y-6%3D0%7D%5C+%7By%2B+2z+%2B+4+%3D0%7D%5C+%7Bx%3D0%7Dend%7Barray%7Dright%5C+left%5Bbegin%7Barray%7D%7Bc%7D+%7Bx%3D0%7D%5C+%7By%3D2%7D%5C+%7Bz%3D-3%7Dend%7Barray%7Dright%5C)
(0; 2; -3)
пересечение с Оxz:
![left[begin{array}{c} {2x+3y-6=0}\ {y+ 2z + 4 =0}\ {z=0}end{array}right\ left[begin{array}{c} {x=3}\ {y=0}\ {z=-2}end{array}right\ left[begin{array}{c} {2x+3y-6=0}\ {y+ 2z + 4 =0}\ {z=0}end{array}right\ left[begin{array}{c} {x=3}\ {y=0}\ {z=-2}end{array}right\](https://tex.z-dn.net/?f=+left%5Bbegin%7Barray%7D%7Bc%7D+%7B2x%2B3y-6%3D0%7D%5C+%7By%2B+2z+%2B+4+%3D0%7D%5C+%7Bz%3D0%7Dend%7Barray%7Dright%5C+left%5Bbegin%7Barray%7D%7Bc%7D+%7Bx%3D3%7D%5C+%7By%3D0%7D%5C+%7Bz%3D-2%7Dend%7Barray%7Dright%5C)
(9; 0; -2)
пересечение с Оху
(9; -4; 0)
пересечение с Оуz:
(0; 2; -3)
пересечение с Оxz:
(9; 0; -2)
Ответ дал:
0
Спасибо!!!
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