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(2012•江西模拟)如图,已知C为△OAB边AB上一点,且AC=2CB,OC=mOA+nOB(m,n∈R),则mn=2929.

题目详情
(2012•江西模拟)如图,已知C为△OAB边AB上一点,且
AC
=2
CB
OC
=m
OA
+n
OB
(m,n∈R),则mn=
2
9
2
9
▼优质解答
答案和解析
AC
=2
CB
,∴
OC
=
OA
+
AC
=
OA
 +
2
3
AB
=
OA
+
2
3
(
OB
OA
 )
=
1
3
 
OA
+
2
3
 
OB

再由
OC
= m
•OA
+ n
•OB
(m,n∈R) 可得 m=
1
3
,n=
2
3
,故mn=
2
9

故答案为:
2
9