问题 填空题
设向量
a
b
满足|
a
|=1,|
a
-
b
|=
3
a
•(
a
-
b
)=0,则|2
a
+
b
|=______.
答案

a
•(
a
-
b
)=0,可得
a
b
=
a
2
=1,

由|

a
-
b
|=
3
,可得(
a
-
b
)2
=3,即
a
2
-2
a
b
+
b
2
=3
,解得
b
2
=4,

(2

a
+
b
)2=4
a
2
+4
a
b
+
b
2
=12,故|2
a
+
b
|
=2
3

故答案为:2

3

选择题
单项选择题