问题 选择题
设向量
a
b
满足|
a
|=1,|
a
-
b
|=
3
a
•(
a
-
b
)=0
,则|2
a
+
b
|
=(  )
A.2B.4C.2
3
D.4
3
答案

|

a
|=1,|
a
-
b
|=
3
可得
a
2
+
b
2
-2
a
b
=3,即
b
2
-2
a
b
=2.

再由

a
•(
a
-
b
)=0 可得
a
2
-
a
b
=0,故有
a
b
=1,
b
2
=4.

|2

a
+
b
|=
(2
a
+
b
)
2
=
4
a
2
+4
a
b
+
b
2
=2
3

故选C.

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