问题 填空题
已知
OA
=(1,1),
OB
=(-1,2)
,以
OA
OB
为边作平行四边形OACB,则
OC
AB
的夹角为______.
答案

∵OACB为平行四边形,

OC
=
OA
+
AC
=
OA
+
OB
=(0,3),
AB
=
OB
-
OA
=(-2,1),

∴cos<

OC
 ,
AB
>=
OC
AB
|
OC
|•|
AB
|
=
0×(-2)+3×1
02+32
(-2)2+12
=
5
5

OC
AB
的夹角为arccos
5
5

故答案为:arccos

5
5

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