How to get the equation of the plane. [read this one]

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To derive the equation of the plane given its vertices, start with the general form ax + by + cz = 0. By substituting the coordinates of the vertices into this equation, relationships between the coefficients can be established. For instance, using the point (1,1,0) leads to the conclusion that a = -b, while using (0,1,1) results in b = -c. This simplifies the equation to x - y + z = 0. Understanding these substitutions is crucial for finding the equation of the plane.
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the above link is the answer to the problem I'm solving. i was wondering how i'd come up with the equation of the plane "x-y+z=0" when only the vertices of the plane are provided in the problem. thanks in advance.
 
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The equation of a plane through the origin is always of the form ax+by+cz=0.
Now you can plug in some points. Say, put in (1,1,0) and you'll find a=-b.
Putting in (0,1,1) b=-c. So the equation reduces to ax-ay+az=0 or x-y+z=0.
 
thanks for the help.
 
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