问题 选择题
在△ABC中,(
BC
+
BA
)•
AC
=|
AC
|2
BA
BC
=3
|
BC
|=2
,则△ABC的面积是(  )
A.
3
2
B.
2
2
C.
1
2
D.1
答案

(

BC
+
BA
)•
AC
=|
AC
|2

(

BC
+
BA
-
AC
)•
AC
=0

则有

BA
AC
=0

∴BA⊥AC 即∠A=90°

|

BC
|=2,则|
AC
|=2cosB,|
AB
|=2sinB

BA
BC
=3,∴4cos2B=3

cosB=

3
2
,sinB=
1
2

S△ABC=

1
2
×1× 
3
 =
3
2

故选:A

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