I want to find some arbitrary point in the plane

$\displaystyle 2x+4y-2z + 10 =0$

Thank you.

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- Aug 14th 2008, 06:34 PMMatteNoobPoints in the plane.
I want to find some arbitrary point in the plane

$\displaystyle 2x+4y-2z + 10 =0$

Thank you. - Aug 14th 2008, 06:55 PMticbol
- Aug 14th 2008, 10:32 PMMatteNoob
Thank you very much. :]

- Aug 15th 2008, 09:29 AMSoroban
Hello, MatteNoob!

Quote:

I want to find some arbitrary point in the plane: .$\displaystyle 2x+4y-2z + 10 \:=\:0$

**intercepts**. .You can "eyeball" the answers!

. . $\displaystyle \begin{array}{cccccccc} \text{Let }y = 0,\:z = 0\!: & 2x + 10 &=& 0 & \Rightarrow & x \:=\: \text{-}5 & \Rightarrow & (\text{-}5,0,0) \\ \\[-4mm] \text{Let }x = 0,\:z = 0\!: & 4y + 10&=& 0 & \Rightarrow & y \:=\: \text{-}\frac{5}{2} & \Rightarrow& \left(0,\:\text{-}\frac{5}{2},\:0\right) \\ \\[-4mm] \text{Let }x = 0,\:y=0\!: & \text{-}2z+10 &=& 0 & \Rightarrow & z \:= \:5 & \Rightarrow & (0,\:0,\:5) \end{array}$

- Aug 15th 2008, 01:32 PMTKHunny
or...

$\displaystyle \frac{x}{-5}\;+\;\frac{y}{-5/2}\;+\;\frac{z}{5}\;=\;1$

They're just kind of staring at you in this form. - Aug 16th 2008, 12:24 PMMatteNoob
Thanks to all of you. I now understand how finding (or checking if) points (are in) the plane. :]