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Консультация № 148703
27.10.2008, 20:59
0.00 руб.
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1
Даны четыре точки А1(4,2,10), А2(1,2,0), А3(3,5,7), А4(2,-3,5).
Составить уравнения:
а) плоскости А1,А2,А3;
б) прямой А1,А2;
в) прямой А4М перпендикулярной плоскости А1А2А3;
г) прямой А3N параллельной плоскости А1А2;
д) плоскости, проходящей через точку А4 перпендикулярную к прямой А1А2;
е) синус угла между прямой А1А4 и плоскостью А1А2А3;
ж) косинус угла между координатной плоскостью 0xy и плоскостью А1А2А3.
Составить уравнения:
а) плоскости А1,А2,А3;
б) прямой А1,А2;
в) прямой А4М перпендикулярной плоскости А1А2А3;
г) прямой А3N параллельной плоскости А1А2;
д) плоскости, проходящей через точку А4 перпендикулярную к прямой А1А2;
е) синус угла между прямой А1А4 и плоскостью А1А2А3;
ж) косинус угла между координатной плоскостью 0xy и плоскостью А1А2А3.
Обсуждение
Неизвестный
31.10.2008, 13:04
общий
это ответ
Здравствуйте, Magictricks!
А1(4,2,10), А2(1,2,0), А3(3,5,7), А4(2,-3,5)
a) (A1,A2,A3)=
|x-4..y-2..z-10|
|1-4..2-2..0-10|=0
|3-4..5-2..7-10|
|x-4..y-2..z-10|
|-3.....0....-10.|=-9(z-10)+10(y-2)+30(x-4)-9(y-2)=-9z+90+10y-20+30x-120-9y+18=0
|-1.....3.....-3..|
30x+y-9z-32=0
b) (А1,А2):
(x-4)/(1-4)=(y-2)/(2-2)=(z-10)/(0-10)
(x-4)/-3=(y-2)/0=(z-10)/-10 - каноническое уравнение прямой А1А2
с) нормальный вектор n(30,1,-9) плоскости А1А2А3 будет направляющим вектором для искомой прямой А4М
(x-2)/30=(y+3)/1=(z-5)/-9=t
x=30t+2
y=t-3
z=-9t+5
e) направляющий вектор n(-3,0,-10) прямой А1А2 будет нормальным для искомой плоскости
-3*(x-2)+0*(y+3)-10*(z-5)=0
-3x+6-10z+50=0
-3x-10z+56=0
А1(4,2,10), А2(1,2,0), А3(3,5,7), А4(2,-3,5)
a) (A1,A2,A3)=
|x-4..y-2..z-10|
|1-4..2-2..0-10|=0
|3-4..5-2..7-10|
|x-4..y-2..z-10|
|-3.....0....-10.|=-9(z-10)+10(y-2)+30(x-4)-9(y-2)=-9z+90+10y-20+30x-120-9y+18=0
|-1.....3.....-3..|
30x+y-9z-32=0
b) (А1,А2):
(x-4)/(1-4)=(y-2)/(2-2)=(z-10)/(0-10)
(x-4)/-3=(y-2)/0=(z-10)/-10 - каноническое уравнение прямой А1А2
с) нормальный вектор n(30,1,-9) плоскости А1А2А3 будет направляющим вектором для искомой прямой А4М
(x-2)/30=(y+3)/1=(z-5)/-9=t
x=30t+2
y=t-3
z=-9t+5
e) направляющий вектор n(-3,0,-10) прямой А1А2 будет нормальным для искомой плоскости
-3*(x-2)+0*(y+3)-10*(z-5)=0
-3x+6-10z+50=0
-3x-10z+56=0
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