问题 解答题
(1)已知平面向量
a
=(1,x),
b
=(2x+3,-x),x∈R.若
a
b
,求出x的值;
(2)已知|
a
|=3,|
b
|=2,
a
b
所成角为60°,求|2
a
+
b
|的值.
答案

(1)若

a
b
,则
a
b
=2x+3-x2=0,∴x=3,或 x=-1.

(2)已知|

a
|=3,|
b
|=2,
a
b
所成角为60°,∴
a
b
=3×2cos60°=3.

|2

a
+
b
|=
(2
a
+
b
)
2
=
4
a
2
+4 
a
b
+
b
2
=
36 +12+4
=
52
=2
13

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