Question

Find the equation of the plane z = mx + ny + b which contains the points (0,0,6), (1,0,-3) and (0,2,5).

Answer 1

The three points give you three equations, which you can solve by your favorite method.
.. 0m +0n +b = 6
.. 1m +0n +b = -3
.. 0m +2n +b = 5

(m, n, b) = (-9, -1/2, 6)
so the equation of the plane can be written as
.. z = -9x -1/2y +6

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In standard form, this would be
.. 18x +y +2z = 12