问题 填空题
已知
OA
=
a
OB
=
b
,|
a
|=2,|
b
|=3,任意点M关于点A的对称点为S,点S关于点B的对称点为N,点C为线段AB中点,则
MN
OC
=______.
答案

由题意可得,AB是△SMN的中位线,∴

MN
=2
AB
=2(
OB
-
OA
).

再由点C为线段AB中点,可得

OC
=
1
2
OB
+
OA
),

MN
OC
=2(
OB
-
OA
)•
1
2
OB
+
OA
)=
OB
2
-
OA
2
=9-4=5,

故答案为 5.

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