问题
解答题
已知向量|
(1)|
(2)
|
答案
(1)由题意可得|
+a
|=b (
+a
)2b
=
=
2+2a
•a
+b
2b
=1;12+2×(-
)+121 2
(2)同理可得|
-b
|=a
=12-2×(-
)+121 2 3
•(a
-b
)=a
•a
-b
2=-a
-12=-1 2
,3 2
故cos<
,a
-b
>=a
=-
•(a
-b
)a |
||a
-b
|a
,3 2
又<
,a
-b
>∈[0,π],a
故
与a
-b
的夹角<a
,a
-b
>=a 5π 6