C. CAU HOI VA BAITAP
§3 TICH CUA VECTO \6l M6T S
1.20. a)m=l; b)m = - 1 ; c)m = A;
d)m= -- ; e) m = 0 ; g) Khdng tdn tai; h) Mgi gia tri cua m diu thoa man.
-* -• |-»l |"*l "* "* I "*l I il~*l I ~*l I il~*l
1.21. a) a = fe => ia| = |fe| va a, fe cung hudng. Ta ed |ma| = |/w||a|, |/nfe| = im||fe|,
dođ |/«a| = |/nfe|.
ma vkmb cimg hudng. Vay ma =mb.
h)ma =mb => |/na| = |mfe| => |a| = |fe| vim^O; ma vkmb cimg hudng =5- a va fe cung hudng.
vay a = fẹ
-* -* I " * l I " * l I I I I "* •*
c)ma = n a => |wa| = |na| => |w| = |n| vi a 9^ 0 ; ma vkna cung hudng => m va n ciing diụ Vay m = n.
1.22. a + a + ... + a = (1 + 1 + ... + l)a =nạ 1.23. GA + GB + GC = d
o GA + 2G/ = 6 (/la trung diim cuaBC)
^GA =-2Gị
Tit đ suy ra ba diim A, G, I thing hang, trong đ GA = 2GI, G nim giiia A
va/.
vay G la trgng tam cua tam giac ABC.
1.24. Ggi G va G lin lugt la trgng tam cua hai tam giac ABC va A 'B 'C'. Ta cd AÁ = AG + GG' + G'Á
BB' = BG + GG' + G'B' CC = CG + GG' + G'C'.
Cdng tiing vl cua ba ding thiic tren ta dugc
JÁ + 'BB' + CC' = 3GG'.
Dođ, nlu AÁ + BB' + CC = 0 thi ^ = 6 hay G s G'.
DS° Cha y : Tii chiing minh tren cung suy ra ring nlu hai tam giac ABC vk
ÁB'Ccd ciing trgng tam thi AA + BB^ + CC = 0.
1.25. (Xem h. 1.45) OC -a +—b OC -a +—b 2 c) Hinh 1.45 Hay tu ve trudng hgp a - 2b. 1.26. (Xem h. 1.46)
a) 'AD = 2Ad = 2(AB + AF) =2AB + 2AF.
b) -AB + -BC = -(AB + 'BC) = -Jc 2 2 2 2 2 2 2 2 -AB+-BC 2 2 = Uc='-ar3=^. 2 2 2
1.27. Ggi F, F lin lugt la trung diim ciia AB, AC. (h. 1.47)
Ta cd tii giac AFME la hinh binh hanh nen AM = J£ + JF = ^JB+-~AC
Cd thi chiing minh cdch khdc nhu sau :
Vi M la trung diim ciia BC ntn 2 AM = AB + AC hay AM = -(AB + AC)
= -AB + -AC. 2 2 1.28. Â = -(AM + AÂ) -AB+-AC 2 3 \' = IAB + -AC (h.1.48) 4 3 Hinh 1.48 1.29. (Xem h. 1.49)
a) BC*' = CA => tii giac ACBC la hinh binh hanh =^ AC'= CB. JB'+ 'AC'= 'BC+ CB = ^ = 0 z:> A la trung diim ciia B ' C . b) Vi tii gidc ACBC la hinh binh hanh
nen CC chiia trung tuyln cua tam giac ABC xuit phdt tir dinh C. Tuong tu nhu vay vdi AÁ, BB'. Do đ AÁ, BB, CC đng quy tai trgng tam G cua tam giic ABC.
1.30. (Xem h. 1.50)
a) BI = BA + AI = -AB + -AC. A
b ) - B / = -
3 3 -AB + -AC A = — A B + -AC
3 2 vay BJ = -BỊ Suy ra ba diim
B, J, I thing hang.
Hgc sinh tu dung diim / .
1.31. MA + MC = 2M0 (vi O la trung diim ciia AC) l4B + ^ = 2M0 (vi O la trung diim ciia BD)
vay MA + MB+ MC + MD = 4M0 (h. 1.51).