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Please Help! Parameterize the plane that contains the three points (3,−5,−2), (10,−12,−10), and (25,0,5). r(s,t)=

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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!
what did you get for vector PQ
btw, this page may help you out see page 3

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I got <7,-7,-8>
Yes i looked at that and Im stll not sure what i dd wrong
how about PR?
ok, so far, so good
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?
i did it twice and got it wrong twice
ok one sec
does it specify at all which variables are the free variables (like x and y or x and z)?
hmm well I managed to find a calculator that will give the equation of the plane
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
so if you let y = s and z = t, then you will get = <-80-25y+21z, y, z> = <-80-25s+21t, s, t>
unfortunately there are many ways to parameterize the plane
can you please provide me with an example
what do you mean
as in please show me a way o parameterize this
well you could take the cross product of vectors PQ and PR
that will give you the normal vector to the plane
what would i do then
what do you get when you do the cross product
gimme a sec
somewhat close, but that's not correct
what is it then?
try it again

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