i j k
1. |i|=|j|=|k|=1
2. i┴J┴k
3. i j k k=ixj
32.
axb= ixj=k ixk=-j jxi=-k jxk=I kxj=-I kxi=j
38.
A(x-x0)+B(y-y0)+C(z-z0)=0
Ax+By+Cz+D=0
39.
Ox- x=-D/A
Oy- y=-D/B
Oz- z=-D/C
ABC- D-
- D=0 ..
- A=0
- =0, =0 ox
- A=0, B=0 Oxy
40.
ó
42.
43.
1. α2||α1 N1||N2
2. α2┴α1 N1N2=0 A1A2+B1B2+C1C2=0
3. N1 N2
46.
47.
2 .
D1 D2
48.
49.
1. l1||l2 S1||S2 =>
2.. l1┴l2 S1┴S2 =>S1S2=0 =>m1m2+n1n2+p1p2
cosA =
.
50.
.
P M*
M*P||N
D=|M*P|=|PrNM0M|=|N*M0M|/|N|=
= =
=
51.
.
- l||α => SN=>NS=0 óAm+Bn+Cp=0
- l┴α => S||N =>
52.
α: Ax+By+Cz+D=0
l:
x=x*+At
y=y*+Bt
z=z*+Ct
α:
l:
l ┴α: m(x-x*)+n(y-y*)+p(z-z*)=0
x=x*+At
y=y*+Bt
z=z*+Ct
53.
.
I
1.
2. B
3. l AB
l:
II
Nb=NaxS={A1,B1,C1}
β: A1x+B1y+C1z+D1=0
x=x*+At
y=y*+Bt
z=z*+Ct
S1=NaxNb
55, 57.
1.
2. x=x0+mt y=y0+nt
3. Ax+By+C=0
4. y=kx+b
58.
1. l1||l2 S1||S2 => k1=k2
2. l1┴l2 S1S2=0=> A1A2+B1B2=0
59.
= tgA=k
2
60.
, (). r , C(a, b) ,
|M0M|=R
=>
61.
, () ( 2 a), .
|
|
|F1F2|=2c |MF1|+|MF2|=2a
a , b , a, b, c a 2 = b 2 + c 2.
e = .
M(x, y) ( ) r1 = a + ex r1 = a ex.
r1 + r2 = 2 a.
, x = .
62.
, () ( 2 ), .
F1 (-c, 0) F2(c, 0) (. 3.3.2),
,
a , b .
. 3.3.2
.
, 2 , 2b, .
.
, .
r1=exa, r2=ex+a. , r2 r1=2a.
r1 =- ex+a, r2=-ex a. , r1 r2 = 2a.
, x y.
, .
63.
, ) .
, a (. 3.3.3),
y2 = 2px.
. 3.3.3
. p>0 , p<0 .
q= |MM|=
y2=2px
) -
- O(0,0,0)
) -
-
- 2
) y2=2px 0x
x2=2py - 0y
y2=zp p=0=> ox p<0