Finding cartesian equation of plane

[thatoneguy6531]

Homework Statement

determine the Cartesian equation of the plane through the points (3,0,1) and (0,1,-1) and perpendicular to the plane with equation x-y-z+1 = 0

Homework Equations

The Attempt at a Solution

Well I know the normal of the plane (a,b,c) dotted with (1,-1,-1) = 0 which gives me a-b-c=0
but other than that I am stuck

 

[Simon Bridge]

You need to write out the description in terms of the maths.
You know the standard form for the cartesian equation of the plane (or the vetor form - whichever you are most comfortable with). So write it out.

That equation has to satisfy some conditions - write out what those mean.

i.e. point (3,0,1) is on the plane - so if you put x=3, y=0, z=1 into the equation, how does it come out?

The rest is simultaneous equations.

 

[HallsofIvy]

(a, b, c).(0, 1,-1)= b- c= 0 so you know b= c. The equation must be of the form a(x- 3)+ by+ b(z- 1)= 0 and you know that x= 0, y= 1, z= -1 must satisfy that: -3a+ b- 2b= 0. Of course, any multiple of (a, b, c) will give the same plane so you can take either a or b to be whatever you like.

 

[thatoneguy6531]

Ok, thanks

 

[Simon Bridge]

Lucky person you - HoI does not normally do people's homework for them...