Hi, I did all the work for this problem but I wanted to ask if someone can expla

Question

Hi, I did all the work for this problem but I wanted to ask if someone can explain to me why r2 is (1,2,1) in this problem. I ask because I would think r2 is (3,5,-2). Also, when I plug in the a for the equation r = r2 + ta for this problem, why do I switch all the signs in the ' a ' coordinates?. I uploaded my picture with all of my work on imgur with the link below and I also wrote little notes to show you what I am referring to. I know the answer is right but I was hoping someone could explain to me the reasoning behind this answer which would help if someone could answer my 2 questions that I asked in this post. Thank you.

http://imgur.com/a/k5fvM

Explanation / Answer

you have taken r = r2 + t a

note that

a = r1 -r2

hence

r = r2 + t(r1 -r2)

r = t * r1 + (1 -t) * r2   

note that sum of coefficient of r1 and r2 is equal to 1

thtat is t + (1-t) = 0

you can also write

r = r1 +t (r2 -r1)

= r1 -t (r1 -r2)

=r1 + k a , where k is -t

note that for any vector will have different t and k . but you could write both ways

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