Cac diem thuoc giao tuyen d co toa do thoa man he:
C2x-y + z + 5 = 0
2x - z + 3 = 0
(1;4;2).
Chox = 0 t h i y = 8, z = 3.
Do do d qua M(0; 8; 3), co VTCP u = (1; 4; 2) nen co phuong trinh tham so va chinh tac la:
t x y - 8 z - 3 8 + 4t ; - = - = 1 4 2 z = 3 + 2t Cach khac: f2x - y + z + 5 = 0 Ta co: 2x + 3 = 0 y = z + 2x + 5 z = 2x + 3
X = t Dat x = t thi y = 8 + 4t, z = 3 + 2t nen phuong Uinh tham s6 la: I y = 8 + 4t
z = 3 + 2t
Ngoai each tim mot chem va VTCP, each tao tham s6. ta co the tim 2
diem tren giao tuyen.
Y I du 3: Viet phuong trinh tham so, chinh tic (neu co) ciia cac duong thang:
x = 1 + 2t
a) Di qua diem A(4; 3; 1) va song song voi duong thing d': < y = -3t
z = 3 + 2t
b) Di qua diem B(-2; 3; 1) va song song voi duong thang j , . x - 2 _ y + l_ z + 2
2 ~ 1 ~ 3
c) Di qua diem C ( l ; 2; -1) va song song voi dudng thang la giao tuyen ciia 2 mat phang x + y - z + 3 = 0 ; 2 x- y + 5 z- 4 = 0.
Giai
a) d' co VTCP u ' = (2; - 3 ; 2) nen dudng thing d qua A, VTCP u = u : co fx = 4 + 2t
x - 4 y- 3 z - 1 phuong trinh: y = 3 - 3 f va
z = 1 + 2t'
b) d' co VTCP u 1 = (2; 1; 3) nen dudng thing d qua B, VTCP u = u' co
x = -2 + 2t
ohuong Uinh: x + 2 _ y - 3 _ z - 1 y = 3 + t
z = 1 + 3t
c) Vecto phap tuyen ciia mat phing x + y - z + 3 = 0 l a n 7 = (1; 1; -1), ciia
mat phang 2x - y + 5z - 4 = 0 la n~2 = (2; - 1 ; 5).
Vecto chi phuong ciia dudng thang c i n tim la:
- (4; -7; -3) r~ — ' i ni n2 = f 1 - 1 - 1 1 1 1