Question

Determine parametric equations for the plane through the points A(2, 1, 1), B(0, 1, 3), and C(1, 3, −2).

Answer 1

If the plane has equation ax+by+cd = m then we need
2a+b+c = m
b+3c = m
a+3b-2c = m
If I have done my math right,
a = m/5, b=2m/5, c=m/5
So, if we set m=5 to clear the fractions, we get
x+2y+z = 5
Now, z = 5-x-2y
So, if we let
x = s
y = t
z = 5-s-2t