Answer:
Explanation:
the points are not coplanar
lets use the first three points to find the equation of the plane:
we need to find two vectors. we can use vectors from (2,-1,2) to (0,0,1) and from (2,-1,2) to (0,5,-2)
vector 1= (-2,1,-1)
vector 2=(-2,6,-4)
now we can find the normal vector:
n= (-2,1,-1) x (-2,6,-4) = (2,6,8)
so the equation containing first three points is:
2x+6y+8z=0
now lets check if the fourth point, (-1,3,-1), lies on this plane:
2(-1) +6(3) +8(-1) =6
since 6 is not equal to 0, the fourth point does not lie on the plane containing the first three points.
therefore, the points are not coplanar.