清华大学微积分习题(下)答案.pdf

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1、

1 1
1.1.....................................1
1.2.....................................4
1.3.....................................8

1.....................................12219
2.1.....................................19
2.2.........................

2、............21
2.3.....................................25
2.4.....................................29

2.....................................33344
3.1.....................................44
3.2.....................................52

3.............................

3、........57467
4.1.....................................67
4.2.....................................69
4.4.....................................74
4.5.....................................77
4.6.....................................80

4...............................

4、......83595
5.1.....................................95
5.2.....................................96
5.3.....................................105
5.4.....................................107
5.5.....................................109
5.6.............................

5、........112ii
5.7.....................................117
5.8.....................................119
5.9.....................................120

5.....................................1236134
6.2.....................................134
6.3...................

6、..................136
6.4.....................................140

6.....................................1461!"#$%&'()Æ*+1.11.M1(4,3,1),M2(7,1,2),M3(5,2,3)

−−−−→
√

7、M1M2

8、=(4−7)2+(3−1)2+(1−2)2=14,−−−−→
√

9、M2M3

10、=(7−5)2+(1−2)2+(2−3)2=6,−−−−→
√

11、M1M3

12、=(4−5)2+

13、(3−2)2+(1−2)2=6,−−−−→−−−−→

14、M2M3

15、=

16、M1M3

17、.∆M1M2M3
2.zA(−4,1,7)B(3,5,−2)−→−−→C(0,0,z).

18、AC

19、=

20、BC

21、,

(−4)2+12+(7−z)2=32+52+(−2−z)2,1414z=,0,0,.993.a(2,−1,0),

22、a

23、=14, b=−2i+3j+6kaa=λb=
−2λi+3λj+6λk.(x,y,z).222

24、a

25、=14λ(−2)+3+6

26、=14,λ=2. 

27、a

28、=−4i+6j+12k,2−x=−4,−1−y=6,0−z=−12x=6,y=−7,z=−12(6,−7,−12).−→4.