I 5x-7y +2z 3=0 vampOxy
94. Dudng thing (d,) CO pt:
[(1 -k)x-ky = ^
ring khi k thay ddi dudng thing d^ ludn: 1) D i qua 1 diem cd' dinh.
2) Thudc mdt mp cd dinh.
95. Viet PT mat phang chiia ducmg thang v6i mat phang: x - 2y | f z + 5 = 0.
x-2z^0
3x-2y + z-3^0
va vuong goc
96. Chimg to rang hai ditcmg thang: x-1 _y + 2 _ z-5 2 ~ - 3 ~ 4 va <
x^7 + 3t y = 2 + 2t z = \-2t
x-2 _ y + 2_ z - 1 Cling thuoc mot mp, vijet PT mp do.
97. Tim PT hinh chieu cua ducmg thang ^ ^ ^
X + 2y + 3z + 4 = 0.
98. Chumg minh rang hai iducmg thang sau day cat nhau: (d,): X = 2t - 3, y = 3l[ - 2, z = 4t + 6.
(d^): X = t + 5, y = -4rtj - 1, z = t + 20. 99. Tinh khoang each giiJj^ hai ducmg thang:
len mp
2x~z-\l = 0
- X - V +i 4 = 0 (da)
3x + y-2 = 0 3y-3z-6 = 0
100. Tim tap hop cac dien'^ M trong khong gian each deu ba diem A ( l ; 1; 1), B ( - l ; 2 ; 0), C(2; - 3 ; 2J).
101. 1) Viet PT ducmg thalng di qua diem A(0; 1; 1), vuong goc vol ducmg
'x + y-z + 2 = 0 x + l = 0
x — \ + 7 z - •>
thang — ^ = - Y ducmg thang •
2) Cho A ( l ; 2; - 1 ) , B('[7; - 2 ; 3) va duomg thang (d) c6 PT:
x^\\_y-2 _z-2
3 '~ -2 ~ 2 ^ •
a) Chiing minh rangi ducmg thang (d) va dudng thang A B cung nam trong mot mp. |
b) Tim diem I e (d) sao cho A I + BI nho nha't
102. Cho mat phang (P): 2x + y + z - 1 = 0, va du6ng thang (d): = y =
Viet PT ctia ducmg, thang qua giao diem ciia (d) va (P), vu6ng goc vdi (d) va nam trcmg (I^).
|03. Chiing to rang ducmg thang: •< ^ , „ nam trong mp: \5x-3y + 2z-5 = ^ , 4x - 3y + 7z - 7 = 0.
04. Cho hai duofng thang c6 PT:
;c + >; = 0
(d,): , (d,):
x + 3y-\ ^
x - > ' + z + 4 = 0 ' ' ' ' [>' + z - 2 = 0 1) Chung to rang hai ducmg thang do cheo nhau.
2) Tinh khoang each gifla chiing.
3) Vie't PT ducmg thang qua M(2; 3; 1) va cat (d,), (dz).
5. Cho hai ducmg thing : (d,)
;c = 2^ +1 y = t^2 vaCdj) z = 3 r - 3 x-s-vl y = ls-3 z = 35 +1 1) Chiing to rang (d,), (d2) la hai ducmg thang cheo nhau. 2) Tinh khoang each gifla (dj) va (d2).
(Dai hoc tong hop Ha Noi, khoi A, nam 1994).
/. Trong khong gian v6i hd toa do Oxyz cho diem M ( l ; 2; -1) va ducmg . x + l _y-2 _ z - 2
thang (d) CO PT:
3 — 2 2 ^
Goi N la diem doi xiing cua M qua ducmg thang (d). Tinh do dai cioan thing M N .
(Dai hoc Bach khoa Ha Noi, nam 1997).
. Trong khong gian, cho hinh binh hanh ABCD c6 hai dinh C(-2; 3; -5), 7
D(0; 4; - 7 ) va giao diem hai duomg cheo M ( l ; 2; - - ) . 1) Viet PT ducmg thing chiia canh AB.
2) Tinh khoang each tiir goc toa do den mp chiia hinh binh hanh. (Dai hoc dan lap Dong D6 Ha Noi, khdi A, 1997).