问题 填空题
已知向量
a
b
满足:|
a
|=1,|
b
|=6,
a
•(
b
-
a
)=2,则
a
b
的夹角为______;|2
a
-
b
|=______.
答案

∵|

a
|=1,|
b
|=6,
a
•(
b
-
a
)=2

a
b
-
a
2
=2

∴1×6cosθ-1=2

∴cosθ=

1
2

∵0≤θ≤π

θ=

1
3
π

|2

a
-
b
|=
(2
a
-
b
)2
=
4
a
2
-4
a
b
+
b
2
=
4-4×1×6×
1
2
+36
=2
7

故答案为:

1
3
π,2
7

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