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Консультация № 105113
11.10.2007, 22:22
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уважаемые эксперты большая прозьба помочь мне с решением
Составить каноническое уравнения прямой,проходяшей через точку А(1,-1,3) и параллельной прямой
{2x-2y+3z-4=0
{x+2y-4z+1=0
Составить каноническое уравнения прямой,проходяшей через точку А(1,-1,3) и параллельной прямой
{2x-2y+3z-4=0
{x+2y-4z+1=0
Обсуждение
Неизвестный
11.10.2007, 22:44
общий
это ответ
Здравствуйте, каныгин дмитрий михайлович!
Сначала составим каноническое уравнение данной прямой
{2x-2y+3z-4=0
{x+2y-4z+1=0.
Выразим x из второго уравнения и подставим в первое. Получим
-6y + 11z – 6 = 0
или
11z = 6y + 6
z/6 = (y+1)/11.
Потом выразим 2y из второго уравнения и подставим в первое:
3x – z – 3 = 0
3x – 3 = z
(x-1)/1 = z/3
(x-1)/2 = z/6.
Получили каноническое уравнение данной прямой:
(x-1)/2 = (y+1)/11 = z/6.
Так как искомая прямая параллельна данной, то её уравнение имеет вид
(x-x0)/2 = (y-y0)/11 = (z-z0)/6,
где x0, y0, z0 — координаты какой-либо точки этой прямой.
Ответ: (x-1)/2 = (y+1)/11 = (z-3)/6.
Сначала составим каноническое уравнение данной прямой
{2x-2y+3z-4=0
{x+2y-4z+1=0.
Выразим x из второго уравнения и подставим в первое. Получим
-6y + 11z – 6 = 0
или
11z = 6y + 6
z/6 = (y+1)/11.
Потом выразим 2y из второго уравнения и подставим в первое:
3x – z – 3 = 0
3x – 3 = z
(x-1)/1 = z/3
(x-1)/2 = z/6.
Получили каноническое уравнение данной прямой:
(x-1)/2 = (y+1)/11 = z/6.
Так как искомая прямая параллельна данной, то её уравнение имеет вид
(x-x0)/2 = (y-y0)/11 = (z-z0)/6,
где x0, y0, z0 — координаты какой-либо точки этой прямой.
Ответ: (x-1)/2 = (y+1)/11 = (z-3)/6.
Форма ответа
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