How would I check this?
Which of the following is not a point on the plane with Cartesian equation ?
a) P(2,0,1)
b) S(0,3,1)
c) R(1,1,1)
d) Q(2,3,4)
if you have the equation of the plane, just see which points satisfy the equation.
This is just like asking which points lie on a line whose equation you have.