Sách Giáo Khoa Hình Học Lớp 10 - Sách Hình học 10 nâng cao

BO GIAO Dgc VA DAO TAO

IRAN VAN HAO (T^ng Chu bi6n) NGUYEN MONG HY (Chii bi6n) NGUviN VAN DOANH - TRAN DlfC HUYEN

HINH HOC

(Tdi bdn ldn thd tu) 10

NHA XUXT BAN GIAO DgC V I | T NAM

K i hieu dung trong sach

• ^ Hoqt dong cua hoc sinh*+ren I6p

Bin quyen thu6c NhS xuat bin Giao due Viet Nam - Bo Giao due va O^o tao.

01-2010/CXB/551-1485/GD Ma sd: CH002T0

cmt/aNG IhnijljlilHii r i|lji I ijiiiji I /

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VECTir

• Vectd *** tong va hieu cua hai vectd *X* Tich cua vectd vdi mot so *t* Toa do cua vectd va toa do cua diem

Trong vqt If ta thuong gap cac dqi lupng co hu6ng nhu luc, vqn toe, ,,. Nguoi ta dung vecto de bieu diin cdc dqi luong do.

I ' ' I J J

§1. CAC DINH NGHIA

1. Khai nl§m vecto

Hinh 1.1

Cac miii ten trong hinh 1.1 bi^u dien hudmg chuydn ddng cua 6t6 va may bay.

Cho doan thang AB. Ne'u ta chon di^m A lam diem ddu, diim B lam diem cud'i thi doan thdng AB co hudng tit A de'n B. Khi dd ta noi AB la mdt doqn thdng CO hudng.

Djnh nghia Vectcx Id mot doqn thdng cd hu&ng.

Vector cd diim 6i\x A, diim cud'i B dugc kf hieu la Ai va doc la "vecto AB". Dl ve vecto AB ta ve doan thang AB va danh 6ia mui ten b 6i\x mut B (h. 1.2a).

Vecto con dugc ki hieu \i a, b, x, y, ... khi khdng cin chi ro diim dSu va diim cud'i cua nd (h. 1.2b).

b)

Hinh 1.2

^ 1 Vdi hai didm A, B phdn bl^t ta co duoc bao nhi§u vecto c6 diim dau vd diim cu6i 1^ A hoac 6.

2. Vecto cung ptiaong, vecto cung tiudng

Ducmg thang di qua diim 6iu va diim cudi ciia mgt vecto dugc ggi la gid cixa vecto dd.

» 2 Hay nhan xet v6 vi trf tifong d6i cQa cac gia cua cac cap vecto sau : AB va CD,

PQy^RS, EF vd PQ (h.1.3).

A

F

B C

E

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Hinh 1.3

Djnh nghia

Hai vecto duoc gpi la cUng phuong ne'u gid ciia chiing song song hodc triing nhau.

Tren hinh 1.3, hai vecto AB va CD cimg phuong va cd ciing hudng di tit

trai sang phai. Ta ndi AB va CD la hai vecto ciing hu&ng. Hai vecto PQ va

RS ciing phuong nhung cd hudng ngugc nhau. Ta ndi hai vecto PQ va RS la hai vecto nguoc hudng.

Nhu vay, neu hai vecto ciing phuong thi chung chi cd thi cung hudng hoac ngugc hudng.

Nhqn xet. Ba diim phan biet A,B,C thang hang khi va chr khi hai vecto AB

va AC ciing phuong.

That vay, ne'u hai vecto AB va AC cung phuong thi hai dudng thang AB va AC song song hoac triing nhau. Vi chiing cd chung diim A nen chiing phai trung nhau. Vay ba diim A, B, C thang hang.

2 Hinh hpc 10-A

Ngugc lai, neu ba diim A, B, C thing hang thi hai vecto AB va AC cd gia triing nhau nen chiing ciing phuong.

«^3 Khang djnh sau dung hay sai;

Neu ba diim phdn bi6t A, 8, C thang hang thi hai vecto ^ va BC cung hirdng.

3. Hai vecto bang nhau

Mdi vecto cd mdt do ddi, 66 la khoang each giiia diim 6iu va diim cud'i cua

vecto dd. Do dai ciia AB dugc ki hieu la IAS|, nhu vay \AB\ = AB.

Vecto cd dd dai bang 1 ggi la vecto don vi.

Hai vecto a \i b dugc ggi la bang nhau niu chiing ciing hudng va cd cung —» - • dd dai, ki hieu a = b .

Cha y. Khi cho trudc vecto a va diim O, thi ta ludn tim dugc mdt diim A duy nha't sao cho OA = a . A 4 Gpi 0 la tdm hinh luc giac deu ABCDEF. Hay chi ra cac vecto bang vecto OA.

4. Vecto - Ichong Ta bie't rang mdi vecto cd mdt diim dau va mdt diim cud'i va hoan toan dugc xac dinh khi biet diim dau va diim cud'i cua nd.

Bay gid vdi mdt diim A hit ki ta quy udc cd mdt vecto ddc biet ma diim 6iu va diim cudi deu la A. Vecto nay dugc ki hieu la AA va ggi la vecto - khdng.

Vecto AA nam tren mgi dudng thang di qua A, vi vay ta quy udc vecto - khdng ciing phuong, ciing hudng vdi mgi vecto. Ta cung quy udc

rang |A4| = 0. Do dd cd thi coi mgi vecto - khdng diu bang nhau. Ta ki hieu vecto - khdng la 0. Nhu vay 0 = AA = BB - ... vdi mgi diim A, B...

2 Hinh hoc 10-B