Question 1009556: Find an equation of the plane that passes through the points
(−1, 0, −4),(2, 1, 8),and(−1, 1, −1).(Suggestion: The equation of a plane can be written as z = ax + by + c.)
Z=
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Let's form two vectors using the three points.
From the first and second,
(2-(-1),1-0,8-(-4))=(3,1,12)
From the first and third,
(-1-(-1),1-0,-1-(-4))=(0,1,3)
Now find the cross product of these two vectors, that will be a vector normal to the plane containing the three points.
N=(3-12)i+(0-9)j+(3-0)k
N=(-9)i+(-9)j+(3)k
N=-3i-3j+k
So then using any of the points (I use the first),
or
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