)
)
)
)
, .
19.
, )
1.
2.
3.
4.
.
20.
.
, .
eAB=|AB| -|AB|
.
1. AB=|AB|cosA
: 1.A- . ABB: |AB| =|AB|cosA
2. A- B=180-A |CC|=|DC|cosB=|DC|cos(Pi-A)=-|DC|cosA =>
=>|DC|=-|DC|cosA
2. AB+=(+)
:
1.1- AB e A2
=|| =|ђ | (+)=|ђ|+|| =|AC|
2.1- A2
=|| =-|ђ | (+)=|ђ|-|| =|AC|
3.k*ea=ka
:
1. K>0 => ka||a =>
=|a|cosA ka=|ka|cosA=|k|
2. K<0 => ka e =Pi-A
eka=|ka|cos(Pi-A)=|k||a|(-cosA)=-|k||a|cosA=kea
21.
ab=|a||b|cosA
1. =|a|cosA=ab/|b|
b=|b|cosA =>ab/|a|
=> ab=|b|ba=|a|b
2. a(b+c)=ab+ac
: ab=|a|ab ac=|a|
(b+c)=b + =>|a|Pra(b+c)=|a|Prab+|a|Pra => a(b+c)=ab+ac
3. (na)b=a(nb)=n(ab)
: a(nb)=|a|Prabn=|a|nPrab=n(ab)
4. ≠0, b≠0 ab=0 .
: 1. a┴b, A=90o => cosA=0, ab=0
5. .
Aa=|a||a|=|a|2=> |a|=
22.
c=axb,
1. |c|=|a||b|sinA
2. c┴a c┴
3. a b
- S=axb
- axb=-bxa
- ax(b+c)=axb+cxa
- (na)xb=ax(nb)=n(axb)
23.
C(axb)=a(bxc)=abc
V=abc
24.
a\\b k≠0? b=ka
:
- b=ka =>b||a, .
- b||a, k=|b|/|a|
||b k=|k|
a||b k=-|k|
=ka =b, .. b=ka, c=ka
a) | c|=|k||a|
b) c||a
c) c||a, k>0
d) c||a, tckb k<0
.
2 .
:
: a=kb a-kb=0
- a≠0, b≠0 a b l1=1, l2=-k
- =0, l1=1, l2=0
≠0, b≠0 ab=0 .
: 1. a┴b, A=90o => cosA=0, ab=0
3 .. 0.
25.
a1 a2an n1 n2nn, ni≠0, n1a1+n2a2++annn=0, n=0
|
|
n a1 a2an, b .. n1 n2nn b=n1a1 +n2a2++nnan
26.
.
2 .
:
: a=kb a-kb=0
- a≠0, b≠0 a b l1=1, l2=-k
- =0, l1=1, l2=0
.
28.