Find a scalar equation of the plane that contains the point P(2,4,1) and is parallel to the plane \(2x_1 + 3x_2 -5x_3 = 6\).

- owlet

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- schrodinger

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- Loser66

just plug the numbers in.

- owlet

|dw:1443664554238:dw|
simplifying that, I got 11, so d =11
will the answer be 2x1 + 3x2 - 5x3 = 11?

- owlet

that's what i did, just wanted to make sure if I'm right

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## More answers

- owlet

i usually have a mistake in vector and scalar equations.. I usually switch them

- owlet

can we fin vector equation from this?

- Loser66

|dw:1443664955587:dw|

- Loser66

|dw:1443665007633:dw|

- owlet

ok thanks for confirming it :)
can we find vector equation from this scalar equation? is it possible?

- Loser66

why not? @chris00 now your turn

- owlet

wait is there even a vector equation for a plane? O.o

- anonymous

haha nice to throw the ball to me

- Loser66

it's not hard, right? all of us know how to do, right?

- anonymous

there is a normal vector equation for the plane...

- anonymous

you can simply read that off

- anonymous

what this represents is

- anonymous

|dw:1443665293308:dw|

- Loser66

hey, guy, give him the easiest way, please.

- anonymous

isn't that just \[(r-r _{o})n=0\]
jeez, its been so long

- owlet

got it, nvm

- anonymous

where n is the normal?

- anonymous

yolo

- anonymous

what did ya do?

- owlet

i am already doing another prob

- anonymous

oh, sorry mate

- anonymous

probs need a refresher since its been like 4yrs ago since I've done this lel

- owlet

try this then:
Verify the triangle inequality and the CAuchy-Schwarz inequality if:
|dw:1443665710601:dw|

- 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

That is the easiest way to find the vector equation from a scalar one.

- Loser66

just replace x2 = lambda 1 and x3 = lambda2

- anonymous

\[|u.v|\le|u||v|\]

- anonymous

i think thats the Cauchy schwartz inequality theorem

- anonymous

pretty straight forward if u apply this, i rekn

- owlet

ok got it..i use the other one:
|dw:1443666019926:dw|

- owlet

thanks.

- anonymous

the triangle inequality?

- anonymous

sus this
http://www.math.lsa.umich.edu/~speyer/417/CauchySchwartz.pdf

- anonymous

u don't need to verify anything if u just proof it using variables

- anonymous

cause a proof applies it for all cases. but its easier with numbers cause you just plug and chug it into formulas

- owlet

it says on the question "Verify the Triangle Inequality"

- 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

i will do that for sure :) I'm studying it right now. Thanks for all your help. Really appreciate it

- anonymous

no problem. good luck :)

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