问题 解答题
已知平面向量
a
b

(Ⅰ)若|
a
|=1,|
b
|=2,|
a
-
b
|=2
,求|
a
+
b
|
的值;
(Ⅱ)若
a
=(1,3),
b
=(-2,m),
a
⊥(
a
+2
b
)
,求m的值.
答案

(I)∵|

a
|=1,|
b
|=2,|
a
-
b
|=2

|

a
-
b
|=
(
a
-
b
)2
=
a
2
-2
a
b
+
b
2
=
5-2
a
b
=2

2

a
b
=1

|

a
+
b
|=
(
a
+
b
)2
=
a
2
+2
a
b
+
b
2
=
6

(II)∵

a
=(1,3),
b
=(-2,m),
a
⊥(
a
+2
b
)

∴(1,3)•(-3,3+2m)=-3+9+6m=0

∴m=-1

单项选择题
单项选择题