IV. TIEN TDM DAY HOC
a) Muc dich: Giiip HS khdc sdu kiín thdc vd ki ndng ve tich cua vecto vdi mdt sd.
- Van dung dugc kiín thde đ trong viec gidi todn.
b) Hudng thuc Men
- Chiia tgi ldp cdc bdi tap: 21 din bdi 25. Cdc bdi tap cdn lgi hudng đn ve nhd.
c) Qud trinh thuc Men
Bai 21.
Hoat đng ciia GV
Cdu hdi 1
Theo quy tdc hinh binh hanh hay
dung OA +aB.
Cdu hdi 2
Theo quy tdc ba diem hay dung
OA - OB.
Hoat đng cua HS
Ggi y trd ldi edu hdi 1
Theo quy tdc hinh binh hanh ta cd:
Dung D sao cho OADB la hinh binh hanh. Khi đ OA + OB = OD.
Ggi y trd ldi cdu hdi 2 'OA-'OB =BẠ
Cdu hdi 3
Theo quy tdc hinh binh hanh hay dung 3OA + 4 0 5 .
Ggi y trd ldi edu hoi 3
Dung OA ' = 30 A, 0B' = 40B,
tiép theo ta dung D' sao cho OÁD'B' la hinh binh hanh, til đ ta cd
30A +40B =0D'.
Trd ldi
0A + 0 5 | = l O A - O ^ I = \BA\ =aV2 ; |30A + 4 0 5 | = 5a ;
V54T — OA + 2 , 5 0 5 — OA + 2 , 5 0 5 4 a ; 'AoA-'-OB 4 1 V6073 28 ạ Bai 22. Hoat đng ciia GV Cdu hdi 1
Hay xac dinh m, n sao cho:
OM = mOA +n0B. , Cdu hdi 2
Hay xac dinh m, n sao cho:
MyV = mOA +nOB ;
Cdu hdi 3
Hay xac dinh m, n sao cho:
AN^mOA +nOB .
Hoat đng ciia HS
Ggi y trd ldi cdu hdi 1
Ta cd OM - — OA, do đ m =— ,n-i)
1 1 Goi y trd ldi cdu hdi 2
Tacd MN = -AB = --OA + -OB,
1 1 1
d o d d m = — ,n = —.
1 1 Ggi y trd ldi cdu hdi 3
Ta cd
AN=-AƠ-AB^-AƠ-OB,
1 1 1
Cdu hdi 4
Hay xac dinh m, n sao cho:
MB =m OA +n OB.
do đ m = - 1 , n = 1
Ggi y trd ldi cdu hdi 4
Ta cd
1
MB^MO + OB = --OA + OB, 1 do đ m —, n= 1. 1 Bai 23. Hoat đng ciia GV Cdu hdi 1
Hay phan tich 2MÂ theo
MD va MC. Cdu hdi 2
Hay phan tfch MD iaeo MA va AD
Cdu hdi 3
Hay phan tich MC theo MB
va 5 C .
Cdu hdi 4
Tir đ riit ra két luan.
Hoat đng cua HS
Ggi y trd ldi edu hdi 1 1MN = MC + MD.
Ggi y trd ldi cdu hdi 2 MD = MA + AD.
Ggi y trd ldi cdu hdi 3 MC = MB + BC.
Ggi y trd ldi cdu hdi 4
1MN = MC + MD^MA + AC + MB + BD =AC+BD.
Bai 24.
GV hudng đn cdu a)
Hoat đng cua GV
Cdu hdi 1
Gpi E la trung diem AB,
tinh: GA + GB.
Cdu hdi 2
Hay tinh GA + GB + GC
hay
Hoat đng cua HS
Ggi y trd ldi cdu hdi 1 GA+GB=1GE
Ggi y trd ldi cdu hdi 2
GA+GB+GC= 1GE+GC=0 ra G la trpng tam. suy Bai 25. Hoat đng ciia GV Cdu hdi 1
Hay bieu thi AB theo a vab.
Cdu hdi 2
Hay lam tuong tu đ'i vdi cac vecto cdn laị
Hoat đng cua HS
Ggi y trd ldi cdu hdi 1 jB--JG + GB^-a + b. Ggi y trd ldi cdu hdi 2
GC = -d-b; BC = -d-lb GA = ld + b.
1
Bai 26.
Hudng đn
Ap dung true tiép bai 24.
Bai 27
Hudng đn
De chiing minh hai tam giac PRT va QSU cd ciing trpng tam, theo bai toan 26, ta cdn
chu:ng minh :YQ + ~RS + flJ = 0. That vay, ta cd :
PQ + RS + TU=-(AC + CE + EA) = 6. 1
Bai 28.
Hudng đn
a) Lay mdt diem O xac dinh nao đ, ta cd :
GA+GB+GC+GD=OA-OG+OB-OG+OC-OG+OD-OG= = 0A + 0B + 0C + 0D-40G.
1 ,TrT
Bdi vay néu GA + GB + GC+ GD ^0 thi OG = -(OA + OB + OC+ 0D).
Vay diem G dupe xac dinh.
Gia su cd diem G' sao cho G'A + G'B + G'C+ G'D = 0.
Suv ra
GA + GB + GC + GD = G'A + G'B + G'C + G'D<^ 4GG' = 0 <:> G = G'.
Nhu vay diem G dupe xac dinh duy nhat.
b) Gpi M, N la trung diem hai canh đ'i nao đ (AB va CD chdng han) va G la trpng
tam tit giac ABCD, ta cd : 0 = GA + GB+ GC+ GD = 2(GM+ GN),suy ra G la
trung diem cua MN. Chiing minh tuong tu ta cd G la trung diem ciia doan thdng nd'i tnmg diem hai canh đ'i AD va BC ; G cung la trung diem ciia doan thang nd'i trung diem hai dudng cheo AC va BD.
c) Ta chpn mdt dinh nao 66 ciia tit giac ABCD, A chang han, va gpi G^ la trpng
tam tam giac BCD tao thanh bdi ba dinh cdn lai cua tii giac. Ta phai chiing minh
rdng trpng tam G ciia tii giac ndm tren doan thang AG^.
That vay, vi G la trpng tam cua tii giac ABCD nen :
GA + GB + GC + GD = 0 (*)
Lai vi G^ la trpng tam tam giac BCD nen : GB + GC+ GD ^3GG^.Nh\i vay tir (*) ta suy ra : GA + 3GG^ = 0. Vay hai vecto GA va GG/^ ngupc hudng, suy ra G ndm tren doan thdng AG^.