anonymous
  • anonymous
Please Help! Parameterize the plane that contains the three points (3,−5,−2), (10,−12,−10), and (25,0,5). r(s,t)=
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I first assigned the points to P Q and R and then found PQ and PR and then put P+u+v and I got <3+7s+22t,-5-7s+5t,-2-8s+7s> but got it wrong!
jim_thompson5910
  • jim_thompson5910
what did you get for vector PQ
jim_thompson5910
  • jim_thompson5910
btw, this page may help you out http://math.harvard.edu/~ytzeng/worksheet/0926_sol.pdf see page 3

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anonymous
  • anonymous
I got <7,-7,-8>
anonymous
  • anonymous
Yes i looked at that and Im stll not sure what i dd wrong
jim_thompson5910
  • jim_thompson5910
how about PR?
anonymous
  • anonymous
22,5,7
jim_thompson5910
  • jim_thompson5910
ok, so far, so good
jim_thompson5910
  • jim_thompson5910
I'm assuming you tried <3+7s+22t,-5-7s+5t,-2-8s+7t>and not <3+7s+22t,-5-7s+5t,-2-8s+7s> right?
anonymous
  • anonymous
i did it twice and got it wrong twice
jim_thompson5910
  • jim_thompson5910
ok one sec
jim_thompson5910
  • jim_thompson5910
does it specify at all which variables are the free variables (like x and y or x and z)?
anonymous
  • anonymous
no
jim_thompson5910
  • jim_thompson5910
hmm well I managed to find a calculator that will give the equation of the plane
jim_thompson5910
  • jim_thompson5910
http://www.wolframalpha.com/input/?i=plane+through+points+%283%2C%E2%88%925%2C%E2%88%922%29%2C+%2810%2C%E2%88%9212%2C%E2%88%9210%29%2C+and+%2825%2C0%2C5%29
jim_thompson5910
  • jim_thompson5910
that equation is -x-25y+21z-80 = 0 -x-25y+21z= 80 solve for x: -x-25y+21z= 80 -x = 80+25y-21z x = -80-25y+21z
jim_thompson5910
  • jim_thompson5910
so if you let y = s and z = t, then you will get = <-80-25y+21z, y, z> = <-80-25s+21t, s, t>
jim_thompson5910
  • jim_thompson5910
unfortunately there are many ways to parameterize the plane
anonymous
  • anonymous
can you please provide me with an example
jim_thompson5910
  • jim_thompson5910
what do you mean
anonymous
  • anonymous
as in please show me a way o parameterize this
jim_thompson5910
  • jim_thompson5910
well you could take the cross product of vectors PQ and PR
jim_thompson5910
  • jim_thompson5910
that will give you the normal vector to the plane
anonymous
  • anonymous
what would i do then
jim_thompson5910
  • jim_thompson5910
what do you get when you do the cross product
anonymous
  • anonymous
gimme a sec
anonymous
  • anonymous
-89i+113j+189k
jim_thompson5910
  • jim_thompson5910
somewhat close, but that's not correct
anonymous
  • anonymous
what is it then?
jim_thompson5910
  • jim_thompson5910
try it again
anonymous
  • anonymous
ok

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