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问题 解答题
已知向量a，b满足|a|=2，|b|=1，a与b的夹角为
π
3
．
（1）求|a+2b|；
（2）若向量a+2b与ta+b垂直，求实数t的值．
答案

（1）∵向量

a
，
b
满足|
a
|=2，|
b
|=1，
a
与
b
的夹角为
π
3
．

∴|

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

=

a
2+4
a
•
b
+4
b
2

=

4+4×2×1×cos
π
3
+4

=2

3
．

（2）∵向量

a
+2
b
与t
a
+
b
垂直，

∴(

a
+2
b
 )• (t
a
+
b
)=0，

∴t

a
2+(2t+1)
a
•
b
+2
b
2=0，

∴4t+(2t+1)×2×1×cos

π
3
+2=0，

解得t=-

1
2
．

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填空题

Tidiness


Tidiness means keeping things out of sight and yet available when wanted. It implies that there is a (1) for everything and that each thing used finds its way (2) to its place by a continuos process, not by a spasmodic (3) . The process depends, however, upon the drawer, cupboard and storage (4) being provided, for lack of which one things may literally have (5) place to go. Like the perambulator and trolley, the luggage and the golfclubs (6) be homeless. The same may be true of the deck-chairs (7) the bulkier plastic toys. As there is no place for them, it is no (8) telling people to put them away. The architect who thus economises on (9) space is apt to claim that a good-sized sitting-room is (10) result. What advantage is there in that, however, (11) half the living-room has to be used for storage The aesthetic (12) depends, in turn, upon storage space. (13) it may be true that no house ever had cupboards enough, (14) are some houses which have practically no cupboards (15) all. In these our choice must lie between chronic (16) and ruthless destruction. That is not to say, however, (17) cupboard space will itself create tidiness. Some people (18) happier, it would seem, in chaos. There is the question, furthermore, (19) the cupboards themselves are tidy. That (20) has been swept out of sight is no proof, in itself, that everything can be found.
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