lai998:最新2019-浙江省瓯海区三溪中学高一数学《平面向量数量积》课件-PPT课件_图文

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2.4.1

a a (1) |a|=|| |a| (2) >0,a a
<0,a a
=0a=0, a=0

a,b,
(a)=() a (+) a=a+a (a+b)=a+b

abOA=a OB=bAOB= 0 180 ab
B


O
0ab O 180ab A 90ab
ab.

A

A

B

O

B

B

b

Oa A

F s
F

S
FW W=|F| |S|cos FS
""

ab |a| |b|cos abab
ab=|a| |b| cos
|a| cos|b| cos ab ba
:0


ab=|a| |b| cos
0 90ab 90 180ab =90ab

abe b
ab | a| | b | c o s a (( 1 2 e) )e a a b a e a |b a | c 0os

bB

(3 ) a b a b |a |b ||;

O

A
B1 a

a b a b |a |b || ;


(4)cos

aa|a|2
ab
| a||b|

|a|

aa

a2

(5 )|a b | |a ||b |

1 |a|=5|b|=4ab =120ab

bB

O

|b|cos B1 a

A

ab

a

|

a

|

ba



|b|cos


1a =0b a b=0
2a 0b ,a b0
3a 0a b =0b=0 4a b=0a b0 5a0a b= b ca=c
6 a a2 |a|2



(1)ab ba
(2)(a)b (ab) a(b)
(3)(ab)c acbc
a b cR

(3)
aba + b c OMMN ON,
(a + b) c = ON |c|

b

a a+b

OM

Nc

= (OM + MN) |c|

= OM|c| + MN|c|



=a c + bc .
(ab )c a(bc)



3 1(ab)2a22abb2 2(ab)(ab)a2b2.
1(ab)2(ab)(ab) (ab)a(ab)b aabaabbb a22abb2.

3 1(ab)2a22abb2 2(ab)(ab)a2b2.
2(ab)(ab)(ab)a(ab)b aabaab
bb a2b2.

a b ab 4 || 6 , || 4 ,

60o ,

a 2 b) ( a 3 b)

5 . |a| 3 ,|b| 4 , k a k b a k b

2.4.2



(1) a b a b cos
2
(2)a a a a

a a

a b a b 0; cos a b .
a b

, aba b



1

i x j y



ab a bcos y A(x1,y1)

B(x2,y2)

i i 1 . j j 1 .

b

a
j

i j j i 0 .

oi

x



ab ab.
a =(x1,y1), b =(x2,y2),

ax1iy1 j bx2iy2 j,

ab(x1iy1 j)(x2iy2 j)

2

2

x1x2i x1y2i jx2y1i jy1y2 j

x1x2 y1y2





y A(x1,y1)

abx1x2y1y2. B(x2,y2) a

b

j

oi

x



2
2
(1)aaa a aa

(1)
2
a (x, y), a x2 y2 , a x2 y2

2

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AB x1 x2 )2 y1 y2 )2

3 1 ab ab0
ax1, y1),b(x2, y2), abx1x2 y1y2 0
2
ax1, y1),b(x2, y2), a//bx1y2 x2y1 0

4
ab 0 180 cos ab
ab
ax1, y1),b(x2, y2),ab (0 180)cos x1x2 y1y2 .
x12 y12 x22 y22 x12 y12 0x22 y22 0.

1 (1 ) a (1,2 3)b , (1,1),
ab ab a b .

(2 ) a(2,3),b(2,4),

ab ab

.

2 A(12)B(23)C(-25)
ABC.
y
C(-2,5)
B(2,3)
A(1,2) x
0

2A52 OAB B=90B.

B37 y B

22

7 3

A

22

O

x



3 1 a =43 b
a b .

2 a 1,0 b(1,2)a //ba .

3 a (3,0)b , (k,5)a b3
4

k.

1 b (3, 4) b(3,4).

55

55

2 2 22 2 22 3 k 5.


1 O A (3,1) O B(0,5)A /C O / B BC A B C C(3, 23 9 )
2A(12)B(40)C(86) D(58)ABCD.
3 a = (12)b = (-32) k a +2 b 2 a - 4b k = - 1.


95191011.


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