1 tÝch v« híng cña hai vect¬ tiÕt 19-20 biªn so¹n vµ thùc hiÖn: hoµng v¨n huÊn...
TRANSCRIPT
![Page 1: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/1.jpg)
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TÝch v« h íng cña hai vect¬
TiÕt 19-20
Biªn so¹n vµ thùc hiÖn:
Hoµng V¨n HuÊn
………………………………………Tæ: To¸n – Tin
Tr êng THPT S¬n §éng sè 1
![Page 2: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/2.jpg)
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KiÓm tra bµi cò
Khi nµo gãc gi÷a hai vect¬
b»ng 00 ? B»ng 1800 ? B»ng 900 ?
![Page 3: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/3.jpg)
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A
B C
KiÓm tra bµi còBµi
to¸n: Cho tam gi¸c ®Òu ABC. TÝnh c¸c gãc:
( AB , AC ) ; ( BA , CA ) ; ( AB , BC )
![Page 4: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/4.jpg)
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Bµi to¸n: Cho tam gi¸c ®Òu ABC. TÝnh
c¸c gãc:
( AB , AC ) ; ( BA , CA ) ; ( AB , BC )
A
B C
KiÓm tra bµi cò
![Page 5: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/5.jpg)
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A
B C
KiÓm tra bµi còBµi
to¸n: Cho tam gi¸c ®Òu ABC. TÝnh c¸c gãc:
( AB , AC ) ; ( BA , CA ) ; ( AB , BC )
![Page 6: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/6.jpg)
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TÝch v« h íng cña hai vect¬
Néi dung bµi häc:
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
2) C¸c tÝnh chÊt cña tÝch v« h íng
3) BiÓu thøc to¹ ®é cña tÝch v« h íng
4) øng dông
TiÕt 19-20
![Page 7: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/7.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬a) §Þnh nghÜa: ( SGK_41 ) Cho hai vect¬ a vµ b kh¸c vect¬ 0. TÝch v« h íng cña hai vect¬ a vµ b lµ mét sè, kÝ hiÖu lµ a . b , ® îc x¸c ®Þnh bëi c«ng thøc sau:
a . b = a. bcos( a , b )Tr êng hîp Ýt nhÊt mét trong hai vect¬ a vµ b b»ng vect¬ 0 ta quy íc a . b =0
![Page 8: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/8.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
Cho a vµ b kh¸c 0 . Khi nµo
a. b = 0 ?
a. b = a . b ? a. b = - a . b ? a. b = 0 a b
a. b = a . b a , b cïng h íng
a. b = - a . b a , b ng îc h íng
![Page 9: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/9.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
TÝnh a . a ?
TÝch a . a = a 2, kÝ hiÖu a 2 , ® îc gäi lµ b×nh ph ¬ng v« h íng cña vect¬ a
![Page 10: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/10.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬b) VÝ dô :
Cho tam gi¸c ®Òu ABC cã c¹nh a vµ träng t©m G. TÝnh c¸c tÝch v« h íng sau:
AB . AC ; AC . BC ; AC . AC
CB . BG ; GB . GC ; GA . BC
![Page 11: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/11.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬b) VÝ dô:
A
. B C
G
AB . AC
=(1/2)a2
= a.a.cos600
= AB . AC cos(AB , AC)
![Page 12: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/12.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
G
A
B C
.
AC . BC =
= a.a.cos600
= AC . BC cos(AC,BC)
![Page 13: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/13.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
G
A
B C
.
AC . AC =
= a2
= AC 2
![Page 14: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/14.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
BG = AG=(2/3)AM= a
3
3
CB. BG =
Ta cã:
= CB . BG cos(CB , BG)= a. a.cos1500
3
3
Suy ra:
G
A
B C
.
M
![Page 15: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/15.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
G
A
B C
.
GB . GC
Ta cã: (GB , GC) = 1200 Suy ra:
M
![Page 16: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/16.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
G
A
B C
.
GA . BC
M
![Page 17: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/17.jpg)
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TÝch v« h íng cña hai vect¬
Cho a vµ b kh¸c vect¬ 0 . Khi nµo
a.b lµ sè ©m?
Lµ sè d ¬ng? B»ng 0 ?
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
![Page 18: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/18.jpg)
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TÝch v« h íng cña hai vect¬
1) §Þnh nghÜa tÝch v« h íng cña hai vect¬
Cho tam gi¸c ®Òu ABC cã c¹nh a vµ träng t©m G. TÝnh c¸c tÝch v« h íng sau:
AB . AC ; AC . BC ; AC . AC
CB . BG ; GB . GC ; GA . BC
TÝnh: AB . AC + AC . BC
CM . BG (M lµ trung ®iÓm cña c¹nh BC)
![Page 19: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/19.jpg)
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TÝch v« h íng cña hai vect¬
2) C¸c tÝnh chÊt cña tÝch v« h íng ( SGK_42 )
Víi ba vect¬ a, b, c bÊt k× vµ mäi sè k ta cã:
a . b = b. a ( TÝnh chÊt giao ho¸n )
a ( b ± c ) = a . b ± a . c ( TÝnh chÊt ph©n phèi )
(ka ). b = k ( a . b )
a2≥0 , a2 = 0 a = 0
![Page 20: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/20.jpg)
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TÝch v« h íng cña hai vect¬
2) C¸c tÝnh chÊt cña tÝch v« h íng ( SGK_42 )
( a + b)2 = a 2 + b2 + 2 a . b
( a – b )2 = a2 + b2 – 2 a . b
( a + b )( a – b ) = a2 – b2
NhËn xÐt:
![Page 21: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/21.jpg)
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TÝch v« h íng cña hai vect¬
2) C¸c tÝnh chÊt cña tÝch v« h íng øng dông:
F1
F2
F
B A
C«ng cña lùc F lµm vËt di chuyÓn tõ A ®Õn B lµ: A = F . AB
H×nh 2.10
![Page 22: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/22.jpg)
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TÝch v« h íng cña hai vect¬
2) C¸c tÝnh chÊt cña tÝch v« h íng
NhËn xÐt: Cho hai vect¬ OA vµ OB. Gäi B’ lµ h×nh chiÕu cña B trªn ® êng th¼ng OA. Ta cã: OA.OB = OA.OB’
øng dông: F1
F2
F
B A
![Page 23: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/23.jpg)
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TÝch v« h íng cña hai vect¬
Cñng cè:+) TÝnh gãc gi÷a hai vect¬
+) TÝnh tÝch v« h íng cña hai vect¬
+) C¸c tÝnh chÊt cña tÝch v« h íng
+) BTVN: Bµi 1, bµi 2 vµ bµi 3 SGK_45
+) Bµi tËp: Chøng minh r»ng ®iÒu kiÖn cÇn vµ ®ñ ®Ó tam gi¸c ABC vu«ng t¹i A lµ BA . BC = AB2
![Page 24: 1 TÝch v« híng cña hai vect¬ TiÕt 19-20 Biªn so¹n vµ thùc hiÖn: Hoµng V¨n HuÊn ……………………………………… Tæ: To¸n – Tin Trêng THPT S¬n §éng](https://reader036.vdocument.in/reader036/viewer/2022081519/56649c875503460f9493f211/html5/thumbnails/24.jpg)
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TiÕt häc ®· kÕt thóc
Xin ch©n thµnh c¸m ¬n c¸c thÇy gi¸o, c« gi¸o vµ c¸c em
häc sinh !
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