![](https://postfiles.pstatic.net/MjAxODAxMTdfMTE1/MDAxNTE2MTg5NDAyNTc5.Qex0mSGta_19ie14dSred9LpcOKc6hjp7PjCN4dtWhkg.Ac3MobdareJYY-DNn_TmTlteSetinSN_4Ijk9mnvyzUg.PNG.ksdskd/3.19.png?type=w1)
[Problem]
Let
a line through the origini n the direction of
![%5Ccombi%20_%7B%201%20%7D%7B%20L%20%7D%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0hvjnvi24rq.jpg)
![%5Ccombi%20_%7B%201%20%7D%7B%20v%20%7D%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0i4d4hu48lm.jpg)
and
the line through b in the direction of
.
![%5Ccombi%20_%7B%202%20%7D%7B%20L%20%7D%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0inmrd9glyt.jpg)
![%5Ccombi%20_%7B%202%20%7D%7B%20v%20%7D%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0j06tc7ta3k.jpg)
To find the the closest points
on the two lines,
![%5Ccombi%20_%7B%201%20%7D%7B%20x%20%7D%5Ccombi%20_%7B%201%20%7D%7B%20v%20%7D%5Cquad%20and%5Cquad%20b%5Cquad%20%2B%5Cquad%20%5Ccombi%20_%7B%202%20%7D%7B%20x%20%7D%5Ccombi%20_%7B%202%20%7D%7B%20v%20%7D%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0o8hpoefyoa.jpg)
write the two equations for the
![%5Ccombi%20_%7B%201%20%7D%7B%20x%20%7D%5Cquad%20and%5Cquad%20%5Ccombi%20_%7B%202%20%7D%7B%20x%20%7D%5Cquad%20%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0p512g177y4.jpg)
that minimize
.
![%7C%7C%5Cquad%20%5Ccombi%20_%7B%201%20%7D%7B%20x%20%7D%5Ccombi%20_%7B%201%20%7D%7B%20v%20%7D-%5Ccombi%20_%7B%202%20%7D%7B%20x%20%7D%5Ccombi%20_%7B%202%20%7D%7B%20v%20%7D-b%7C%7C%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0wo0xslhw7w.jpg)
Solve for x if
= (1,1,0)
= (0,1,0) , b = (2,1,4)
![%5Ccombi%20_%7B%201%20%7D%7B%20v%20%7D%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0i4d4hu48lm.jpg)
![%5Ccombi%20_%7B%202%20%7D%7B%20v%20%7D%20](https://ssl.pstatic.net/images.se2/smedit/2018/1/17/jcj0j06tc7ta3k.jpg)
[Solution]
이 포스팅은 길버트 스트랭의 선형대수학과 그 응용 4판 문제풀이에 대한 것입니다.
질문은 댓글로 남겨주시면 아는 한도에서 성실하게 답변해드리겠습니다.
That was my answer for problem 3.3.18
Linear Algebra and its Application 4th edition (international edition)