问题 解答题
已知向量
a
b
的夹角为60°,且|
a
|=2,|
b
|=1,若
c
=
a
-4
b
d
=
a
+2
b
,求
(1)
a
b

(2)|
c
+
d
|.
答案

(1)

a
b
=|
a
|×|
b
|cos60°
=2×1×
1
2
=1;

(2)∵

c
+
d
=2
a
-2
b
,∴|
c
+
d
|
=
(
c
+
d
)2
=
(2
a
-2
b
)2
=2
a
2
-2
a
b
+
b
2
=2
22-2×1+12
=2
3

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