问题 选择题
若等边△ABC的边长为2
3
,平面内一点M满足
CM
=
1
3
CB
+
1
3
CA
,则
MA
MB
=(  )
A.-2B.2C.-2
3
D.2
3
答案

CM
=
1
3
CB
+
1
3
CA

MA
=
CA
-
CM
=
CA
-(
1
3
CB
+
1
3
CA
)=
2
3
CA
 - 
1
3
CB

MB
=
CB
-
CM
=
CB
-(
1
3
CB
+
1
3
CA
) =
2
3
CB
-
1
3
CA

MA
MB
=(
2
3
CA
-
1
3
CB
) • (
2
3
CB
1
3
CA
)=
5
9
CA
 •
CB
-
2
9
|
CA
|
2
 -
2
9
|
CB
|
2
=
5
9
×|
CA
| ×|
CB
| ×cos60°-
2
9
(2
3
)
2
-
2
9
(2
3
)
2

=

5
9
×2
3
×2
3
×
1
2
-
2
9
×12-
2
9
×12=
30
9
-
48
9
=-2

故选A

单项选择题 A3/A4型题
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