Given the points A(1,1,2), B(1,2,1), C(2,1,1) which lie in plane x+ay+bz+c=0, what is the plane?

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The points A(1,1,2), B(1,2,1) and C(2,1,1) lie in plane x+ay+bz+c=0

To determine the value of a, b and c, solve the set of equations:

1 + a + 2b + c = 0 ...(1)

1 + 2a + b + c = 0 ...(2)

2 + a + b + c = 0 ...(3)

(1) - (3)

=> -1 + b = 0

=> b = 1

(1) - (2)

=> -a + b = 0

=> -a + 1 = 0

=> a = 1

Substitute a = 1 and b = 1 in (3)

=> 2 + 1 + 1 + c = 0

=> c = -4

The equation of the plane is x + y + z - 4 = 0

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