IV. TIEN TDM DAY HOC
Bfll TflP TRflC NGHIEM
Chpn phuang an tra ldi diing cho cac cau sau :
Cau 1 .• Cho AAeC, trpng tam G, I la trung diem cua BC. Ta cd
(a)AG = 3/G; (h) AB +AC = GB + GC
(c) A 5 + A C = 2A7; (d) 7 G + Z S + 7 C = 0.
Trd ldi: Phuong an diing; (c).
Cau 2 .• Cho hinh binh hanh ABCD, tam O ta cd :
(a)A6 + DA = 2 0 A ; (b) AB + fiC = 2 C 0 ;
(c)AB + BC + CD = 3A0; (6) AB + AD = 1A0. Trd ldi: Phuong an diing : (d).
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Cau 3 .• Cho doan thang AB va M la mdt diem thudc doan AB sao cho AM = —AB.
So k thoa man MA = kMB. Sd k cd gia tri la
(a)^; ( b ) ^ ; 5 4 ( c ) - ^ ; ( d ) - ^ .
5 4
Trd ldi: Phuong an diing : d).
Cau 4 .• Cho vecto M = la-5b. Vecto đ'i cua vecto u la :
(a)-la + 5b; (h)-la-5b; (c)la + 5b; (6)-(-la + 5b).
Trd ldi: Phuang an diing : (a).
Cau 5 .• Cho AABC, trpng tam G. Cac diem D, E, F tuang iing la trung diem cua
BC, CA, AB. Dat w = A£ va V = AF
a) Phan tich AI (I la trung diem cua AD) theo u va v la :
(a)-(u + v); (h)-(u-v);
Ạ ^
(c)-('v-w); (d) M + -V. 2 2 ,
Trd ldi: Phuong an diing: (a).
b) Phan tich cua AG theow, v la :
2 - 4 - 4 - 2 -(a)-M + - v ( b ) - M + - v (a)-M + - v ( b ) - M + - v
( C ) ^ ( M + V) ( d ) - ( M - v ) ,
Trd ldi: Phuang an diing : (c).
c) Phan tich ciia vecto DE theoH, v la:
(a)D£: = (-lJM + 0.v (b) D £ = (-l)v + 0.M
(c)DE = u + v (6) DE = -(u + v). Trd ldi:: Phuong an diing : (b).
d) Phan tfch vecto DC theo hai vecto u va v va :
(a)DC = M + v (b)DC = v-M
(e)DC = M-v (6) DC = -(u + v).
Trd ldi: Phuong an diing :(e).
Cau 6 .• Cho AASC, M thudc canh BC sao cho MB = IMC. Dat M = A 5 , v = AC
Phan tfch vecta AM theo hai vecto M , v ta duoc
(a)AM = M + v (b)AM = -M + - v 2 3 1 - 2 - ,., ^ ^ 1 - 2 -
(c) AM = -u — V (d) AM = - w + — V.
3 3 3 3
Cau 7 .• Cho AABC va AA S'C 'cd ciing trpng tam. Ta cd
(a) AÁ + BB' + CC = AC'; (b) AÁ + BB' + CC = 0
(c) AÁ+ B5' + CC' = 3AG (Gia trpng tam AA5C)
(6) AÁ + BB'= CC'
Trd ldi: Phuong an diing : (b).
Cau 8 .• Cho luc giac deu ABCDEF, tam O, canh ạ Dp dai ciia vecto
-JB + -BC la:
2 2
(a)aV^ ( b ) ^
(c)2aV3 (d) — : 4
Trd ldi: Phuong an diing : (b).
Cau 9 .• Cho AABC, trung tuyen AM, I la trung diem ciia AM va K la diem thoa
man AK = — AC .Tac6 :
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(a) B, I, K thang hang; (b) B, I, K khdng thang hang
(c) 4'BK = 3'B1; (6) BK = ÍBA + 3'BC.
Trd ldi: Phuong an diing : (a).
Cau 10 .• Cho AA5C, / thudc canh AC sao cho CI = — CA, J la diem thoa man
4 Ij = -JC--JB.Tac6: 2 3 (a)Tl = -Jc + -JB; (h)Tl=-JC + JB 1 3 4 (C)TI = -JC-JB; (6)Tl = 3BJ. 4
Trd ldi: Phuong an diing : (c).