Three points are given: P = (2,1,0) , Q = (1,0,1) , R = (3,2,-1).
I'm supposed to find the plane that goes through P, Q, R in the form Ax + By + Cz = D.
My attempt:
M : (x,y,z) = P + t*PQ + s*PR , s,t ∈ R.
PQ = Q - P = (-1,-1,1) , PR = R - P = (1,1,-1).
This gives me a system of equaton where I use the elimination method to find out what the coefficients A, B, C and D are equal to, but I'm stuck at the second step:
x = 2 - t + s
y = 1 - t + s
z = + t - s
<=>
x = 2 - t + s
-x + y = - 1
x + z = 2
Did I do something wrong? / How do I proceed from here?