Three Dimensional Geometry

Question

Find the equations of the planes that passes through three points:
(1, 1, 0), (1, 2, 1), (–2, 2, –1)

Solution

The given points are (1,1, 0), (1, 2,1), (–2, 2, –1).
These points are not collinear.
The equation of plane passing through these points is
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or $open vertical bar table row cell straight x minus 1 end cell cell straight y minus 1 end cell straight z row 0 1 1 row cell negative 3 end cell 1 cell negative 1 end cell end table close vertical bar space equals space 0$
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