# Thread: Finding Cartesian form for a plane in R3 in parametric form

1. ## Finding Cartesian form for a plane in R3 in parametric form

Hi,

I'm stuck on a really simple question of changing a plane to a Cartesian form.

<x,y,z>=<1,2,3>+a<-1,1,-1>+b<1,0,1>

Here's what I have so far:

x=1-a+b
y=2+a
z=3-a+b

x-z=-2

From here, I'm stuck finding y in terms of anything. Any attempt to find y in terms of x and z just leads to circles.

Please help!

Thank you!

2. ## Re: Finding Cartesian form for a plane in R3 in parametric form

Originally Posted by JDoops
Hi,

I'm stuck on a really simple question of changing a plane to a Cartesian form.

<x,y,z>=<1,2,3>+a<-1,1,-1>+b<1,0,1>

Here's what I have so far:

x=1-a+b
y=2+a
z=3-a+b

x-z=-2

From here, I'm stuck finding y in terms of anything. Any attempt to find y in terms of x and z just leads to circles.

Please help!

Thank you!
you have the correct answer

$x - z = -2$

$a=1,~b=0,~c=-1,~d=-2$