owlet
  • owlet
Find a scalar equation of the plane that contains the point P(2,4,1) and is parallel to the plane \(2x_1 + 3x_2 -5x_3 = 6\).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Loser66
  • Loser66
just plug the numbers in.
owlet
  • owlet
|dw:1443664554238:dw| simplifying that, I got 11, so d =11 will the answer be 2x1 + 3x2 - 5x3 = 11?
owlet
  • owlet
that's what i did, just wanted to make sure if I'm right

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owlet
  • owlet
i usually have a mistake in vector and scalar equations.. I usually switch them
owlet
  • owlet
can we fin vector equation from this?
Loser66
  • Loser66
|dw:1443664955587:dw|
Loser66
  • Loser66
|dw:1443665007633:dw|
owlet
  • owlet
ok thanks for confirming it :) can we find vector equation from this scalar equation? is it possible?
Loser66
  • Loser66
why not? @chris00 now your turn
owlet
  • owlet
wait is there even a vector equation for a plane? O.o
anonymous
  • anonymous
haha nice to throw the ball to me
Loser66
  • Loser66
it's not hard, right? all of us know how to do, right?
anonymous
  • anonymous
there is a normal vector equation for the plane...
anonymous
  • anonymous
you can simply read that off
anonymous
  • anonymous
what this represents is
anonymous
  • anonymous
|dw:1443665293308:dw|
Loser66
  • Loser66
hey, guy, give him the easiest way, please.
anonymous
  • anonymous
isn't that just \[(r-r _{o})n=0\] jeez, its been so long
owlet
  • owlet
got it, nvm
anonymous
  • anonymous
where n is the normal?
anonymous
  • anonymous
yolo
anonymous
  • anonymous
what did ya do?
owlet
  • owlet
i am already doing another prob
anonymous
  • anonymous
oh, sorry mate
anonymous
  • anonymous
probs need a refresher since its been like 4yrs ago since I've done this lel
owlet
  • owlet
try this then: Verify the triangle inequality and the CAuchy-Schwarz inequality if: |dw:1443665710601:dw|
Loser66
  • Loser66
2x1+3x2-5x3=11 \(x_1= 11/2 - (3/2)x_2 +(5/2)x_3\) Hence vector equation is \(\vec x= \left[\begin{matrix}(11/2)-(3/2)x_2 +(5/2)x_3\\x_2\\x_3\end {matrix}\right]\) Now, turn to \(\vec x= \left[\begin{matrix}11/2\\0\\0\end{matrix}\right]+ x_2\left[\begin{matrix}(-3/2)\\1\\0\end{matrix}\right]+x_3\left[\begin{matrix}(5/2)\\0\\1\end{matrix}\right]\)
Loser66
  • Loser66
That is the easiest way to find the vector equation from a scalar one.
Loser66
  • Loser66
just replace x2 = lambda 1 and x3 = lambda2
anonymous
  • anonymous
\[|u.v|\le|u||v|\]
anonymous
  • anonymous
i think thats the Cauchy schwartz inequality theorem
anonymous
  • anonymous
pretty straight forward if u apply this, i rekn
owlet
  • owlet
ok got it..i use the other one: |dw:1443666019926:dw|
owlet
  • owlet
thanks.
anonymous
  • anonymous
the triangle inequality?
anonymous
  • anonymous
sus this http://www.math.lsa.umich.edu/~speyer/417/CauchySchwartz.pdf
anonymous
  • anonymous
u don't need to verify anything if u just proof it using variables
anonymous
  • anonymous
cause a proof applies it for all cases. but its easier with numbers cause you just plug and chug it into formulas
owlet
  • owlet
it says on the question "Verify the Triangle Inequality"
anonymous
  • anonymous
yea, probs best to just verify then. i was just giving you a proof for you to understand that it word for any case. perhaps you can read that in your own time to familiarise it for yourself
owlet
  • owlet
i will do that for sure :) I'm studying it right now. Thanks for all your help. Really appreciate it
anonymous
  • anonymous
no problem. good luck :)

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