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

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ranyai12Best ResponseYou've already chosen the best response.0
I first assigned the points to P Q and R and then found PQ and PR and then put P+u<PQ>+v<PR> and I got <3+7s+22t,57s+5t,28s+7s> but got it wrong!
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
what did you get for vector PQ
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
btw, this page may help you out http://math.harvard.edu/~ytzeng/worksheet/0926_sol.pdf see page 3
 9 months ago

ranyai12Best ResponseYou've already chosen the best response.0
Yes i looked at that and Im stll not sure what i dd wrong
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
how about PR?
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
ok, so far, so good
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
I'm assuming you tried <3+7s+22t,57s+5t,28s+7t>and not <3+7s+22t,57s+5t,28s+7s> right?
 9 months ago

ranyai12Best ResponseYou've already chosen the best response.0
i did it twice and got it wrong twice
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
does it specify at all which variables are the free variables (like x and y or x and z)?
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
hmm well I managed to find a calculator that will give the equation of the plane
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
that equation is x25y+21z80 = 0 x25y+21z= 80 solve for x: x25y+21z= 80 x = 80+25y21z x = 8025y+21z
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
so if you let y = s and z = t, then you will get <x, y, z> = <8025y+21z, y, z> <x, y, z> = <8025s+21t, s, t>
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
unfortunately there are many ways to parameterize the plane
 9 months ago

ranyai12Best ResponseYou've already chosen the best response.0
can you please provide me with an example
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
what do you mean
 9 months ago

ranyai12Best ResponseYou've already chosen the best response.0
as in please show me a way o parameterize this
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
well you could take the cross product of vectors PQ and PR
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
that will give you the normal vector to the plane
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
what do you get when you do the cross product
 9 months ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
somewhat close, but that's not correct
 9 months ago
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