Kióứm tra baỡi cuợ
Goỹi M vaỡ N lỏửn lổồỹt laỡ trung õióứm cuớa caùc caỷnh AB vaỡ
CD cuớa tổù giaùc ABCD. Chổùng minh rũng:
Baỡi toaùn:
2MN BC AD= +
uuuur uuur uuur
C/m:
MD MC+ =
uuuur uuuur
( ) ( )
MA AD MB BC+ + + =
uuur uuur uuur uuur
( ) ( )
AD BC MA MB+ + + =
uuur uuur uuur uuur
BC AD+
uuur uuur
Ta coù:
(õpcm)
2MN =
uuuur
1 1
2 2
MN BC AD= +
uuuur uuur uuur

D
C
B

Cho hai vectồ khọng cuỡng phổồng vaỡ .
a
r
b
r
Khi õoù, moỹi vectồ õóửu coù thóứ bióứu thở mọỹt caùch duy
nhỏỳt qua hai vectồ vaỡ , nghộa laỡ coù duy nhỏỳt cỷp
sọỳ m vaỡ n sao cho:
x
r
a
r
b
r
nbx ma= +
rr r
Dan. l

x
r
C
x
r
C
Chổùng minh:
b
r
a
r
A

0x a nb= +
r r r

Nóỳu cuỡng phổồng vồùi
x
r
b
r
.
O
A
a
r
B
b
r
b
r
a
r
x
r
coù sọỳ n sao cho
thỗ
.
O