C. CAU HOI VA BAITAP
§2 T6NG VA HIEU CUA HAI VECTO
1.8. 1.9. 1.10. 1.11. 1.12. 1.13. AB + BC + CD + DE = AC + CD + DE = AD + DE = AẸ
JB-CD = A C - ^ <:> JB + ^ = JC + CD <» AD = AD. Nhu vay he
thiic cin chung minh tuong duong vdi ding thiic diing.
a)OA + OB = 0=>OB = - ^ ^ OB = OA, ba diim A, O, B thing hang va diim O d giiia A va B. Suy ra O la trung diim ciia AB.
b) 0^ + ^3 = 0 => OB = 0 ^B = 0.
Trong tam gi^c diu ABC, tam O ciia dudng trdn ngoai tilp ciing la trgng
tam ciia tam giac. vay OA + OB + OC = 0.
OA + OB + OC + OD = (OA + OC) + (OB + OD) = 0 + 0 = 0. FMII BE vi FM la dudng trung binh
ciia tam giac CEB.
Ta cd EA = EF. Vay EN la dudng trung binh cua tam giac AFM. Suy ra N la trung diim cua AM. Vay
^ = -1^} (h.1.41).
M B Hinh 1.41 Hinh 1.41
1.14. a) MA-MB = BA <^ BA = BẠ Y&y mgi diimM diu thoa man he thiic a). b) ]^-JiB = 'AB <» BA = AB <:> A s B, vd H. Vay khdng cd diim M nao
thoa man he thiic b).
c) MA + MB = 0 -» MA = -MB. Vay M la trung diim ciia doan thing AB. 1.15. Ve hinh binh hanh CADB. Ta cd CA + CB = CD,
dođ |CA + CB| =CD.
Vi CA-CB = BA, dođ | C A - C B | =BẠ
Til |CA + C B | = | C A - C B | suý ra
CD = AB(h. 1.42).
vay tii giac CADB la hinh chii nhat. Ta cd tam giac ACB vudng tai C.
Hinh 1.42 1.16. l^B+ ^+ CD = AE-DE <;=> AC+ CD = AE+ 'ED <^ JD = JD. 1.17. dA + OB = dC trong đ OACB la hinh binh hanh. OC la phan giac gdc
AOB khi va chi khi OACB la hinh thoi, turc la OA = OB. 1.18. F^+F^=OA
F^+F^ = 0A= IOOV3.
Hinh 1.43
Vay cudng đ ciia hgp luc la 100V3N(h.l.43).
1.19. (Xem h. 1.44)
a)AB = 0B-0A DC=0C-0D.
Vi ^8 = 1^6 nen tacd OB-OA = dC-OD. vay OB + OD = dA + OC.
b) Tii giac AMOE la hinh binh
hanh nen ta cd MF = MA + MO (1) Tii giac OFCÂ la hinh binji
hanh nen ta cd Fiv = FO + FC (2) (adsbygoogle = window.adsbygoogle || []).push({});
Tii(l)vă2)suyra JIE + JN = 'MA + 'MO + 'Fd + 'FC
= (MA + 'Fd) + (Md + 'FC) = BA + ^ = lBD {vĩFd = 'BM,'Md = 'BF).